LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


t 


OTHER  WORKS 
BY  THE   SAME  AUTHORS 


DYNAMO    ELECTRIC   MACHINERY; 

ITS  CONSTRUCTION,  DESIGN, 

AND  OPERATION 

VOL.  I.    DIRECT  CURRENT  MACHINES,  Eighth 

Edition,   Completely  Rewritten,  8vo.     Cloth, 

Illustrated.     338  pp.  Net,  $2.50. 


VOL.  II.    ALTERNATING  CURRENT  MACHINES, 

Eighth   Edition,  Completely  Rewritten,  8vo. 
Cloth,     Illustrated.     366  pp.  Net,  $2.50. 


ELECTRIC 

TRACTION  AND  TRANSMISSION 
ENGINEERING 


BY 

SAMUEL    SHELDON,    A.M.,  PH.D.,  D.Sc. 

*  t 

PROFESSOR  OF  PHYSICS  AND  ELECTRICAL  ENGINEERING  AT  THE  POLYTECHNIC  INSTITUTE 

OF  BROOKLYN,   AND    PAST-PRESIDENT  OF  THE  AMERICAN 

INSTITUTE  OF  ELECTRICAL  ENGINEERS 

AND 

ERICH    HAUSMANN,    E.E.,  M.S. 

INSTRUCTOR  IN  PHYSICS  AND  ELECTRICAL  ENGINEERING  AT  THE  POLYTECHNIC 

INSTITUTE  OF  BROOKLYN,   AND  ASSOCIATE  OF  THE  AMERICAN 

INSTITUTE  OF  ELECTRICAL  ENGINEERS 


With  127  Illustrations 


NEW  YORK: 

D.    VAN    NOSTRAND    COMPANY 

23  MURRAY  AND  27  WARREN  STS. 

1911 


COPYRIGHT,  1911,  BY 
D.  VAN  NOSTRAND   COMPANY 


Stanbopc  ipress 

F.  H.  GILSON  COMPANY 
BOSTON.  U.S.A. 


PREFACE. 


THE  ultimate  purpose  of  nearly  all  the  professional 
efforts  of  an  engineer  is  the  attainment  of  efficiency  in  the 
utilization  of  labor,  capital,  and  energy.  To  attain  the 
highest  efficiency  in  the  construction  and  the  subsequent 
operation  of  a  complete  installation  requires  a  knowledge 
of  the  facts  and  a  familiarity  with  the  laws  pertaining  to 
these  three  factors.  Decisions  as  to  the  selection  of  the 
type  and  the  dimensions  of  an  element,  often  attributed 
to  the  exercise  of  good  judgment,  are  generally  the  specific 
results  of  the  correct  application  of  laws  to  all  pertinent 
facts. 

The  number  of  facts  to  be  considered  in  determining  the 
final  elements  of  a  complete  electric  traction  system  is 
enormous.  As  a  consequence  students  and  young  engineers 
become  bewildered  and  are  unable  to  discriminate  as  to  the 
pertinency  or  necessity  of  specific  details.  To  meet  this 
condition  the  present  text  has  been  prepared,  it'  being 
believed  that  no  other  single  published  book  meets  it. 

The  book  attempts  to  present  a  perspective  view  of  the 
design  of  a  complete  railway  installation,  from  the  cars 
to  the  power-station,  to  indicate  the  nature  and  sequence  of 
the  various  entailed  problems,  and  to  suggest  or  illustrate 
methods  for  their  solution. 

In  preparing  the  text  the  determination  of  what  to  omit 
has  involved  nearly  as  much  effort  as  of  what  to  include. 

v 

224494 


VI  PREFACE 

A  descriptive  treatment  of  specific  forms  of  structures  has 
been  avoided.  On  the  other  hand,  a  number  of  numerical 
illustrations  of  the  calculation  of  economic  magnitudes  has 
been  given.  Again,  the  inevitable  future  extensive  use  of 
hyperbolic  functions  has  claimed  for  them  a  brief  but 
comprehensive  exposition  and  their  utility  is  demonstrated 
in  connection  with  calculations  relating  to  electric-wave 
propagation. 

Appreciation  is  hereby  expressed  of  the  services  of  Mr. 
G.  I.  Rhodes  in  making  helpful  suggestions  and  in  reading 
the  proofs  of  the  sections  on  economic  determinations. 

POLYTECHNIC  INSTITUTE,  BROOKLYN,  N.Y. 
May  i,  1911. 


CONTENTS. 


CHAPTER  I. 

DETERMINATION  OF  THE  NUMBER  AND  SIZE  OF  CARS  FOR  AN 
URBAN  ROAD. 

ART.  PAGE 

1.  The  Engineer's  Problem i 

2.  Types  of  Service i 

3.  Length  of  Track 2 

4.  Receipts 4 

5.  Number  of  Cars 4 

6.  Size  of  Cars 8 

7.  Numerical  Example 12 

Problems 14 

CHAPTER  II. 
TRACTIVE  EFFORT  REQUIRED  FOR  CAR  PROPULSION. 

8.  Train  Resistance 15 

9.  Grades 19 

10.  Curves 19 

11.  Acceleration 21 

12.  Braking 22 

Problems 24 

CHAPTER  III. 
TYPES  AND  PERFORMANCE  CURVES  OF  MOTORS. 

13.  Traction  Motors 25 

14.  Direct-current  Motors 26 

15.  Alternating-current  Motors 27 

16.  Methods  of  Drive 40 

17.  Motor  Curves 43 

Problems 49 

vii 


viii  .  CONTENTS. 

CHAPTER  IV. 

SPEED  CURVES. 

ART.  PAGE 

18.  Motor  Limitations 50 

19.  Motor  Capacity 51 

20.  Speed 51 

21.  Typical  Speed  Curves 52 

22.  Data  for  Plotting  Speed  Curves 53 

23.  Plotting  Speed  Curves 56 

24.  Numerical  Example 59 

25.  Distance  Curves 66 

26.  Speed  Curve  Plotting  with  Grades  and  Curves 67 

Problems 72 

CHAPTER   V. 
RAILWAY  MOTOR  CONTROL. 

27.  Direct-current  Control 74 

28.  Rheostatic  Method 74 

29.  Series-parallel  Method 75 

30.  Starting  Resistances 78 

31.  Numerical  Example 87 

32.  Alternating-current  Control 89 

33.  Induction  Regulators 89 

34.  Compensators 91 

35.  Induction  Motor  Control 95 

36.  Controllers 102 

Problems - 109 

CHAPTER   VI. 

ENERGY  CONSUMPTION. 

37.  Current  Curves in 

38.  Average  and  Effective  Currents 112 

39.  Numerical  Example 113 

40.  Effective  Motor  Current  for  a  Trip 116 

41.  Voltage  Curve 118 

42.  Motor  Heating 118 

43.  Energy  for  Direct-current  Propulsion 120 

44.  Energy  for  Alternating-Current  Propulsion 121 


CONTENTS.  IX 

ART-  PAGE 

45.  Effect  of  Operating  Conditions  on  Energy  Consumption 124 

46.  Gear  Ratio I3o 

Problems ^2 

CHAPTER   VII. 
THE  DISTRIBUTING  SYSTEM. 

47.  Classification  of  Conductors 133 

48.  Contact  Conductors 134 

49.  Branches !39 

50.  Collecting  Devices 140 

51.  Supplementary  Conductors 142 

52.  Graphic  Time-table 147 

53.  Feeders 151 

54.  Track  Rails 155 

55.  Negative  Track  Feeders 157 

56.  Electrolytic  Surveys 161 

57.  Alternating-current  Distribution 164 

Problems 164 

CHAPTER  VIII. 

SUBSTATIONS. 

58.  Types  of  Substations 166 

59.  Direct  Currents  Received  and  Delivered 166 

60.  Alternating  Currents  Received  and  Delivered 168 

61.  Alternating  Currents  Received  and  Direct  Currents  Delivered  . . .  169 

62.  Location  of  Substations 175 

63.  Numerical  Illustration 186 

64.  Auxiliary  Storage  Batteries 188 

65.  Arrangement  of  Apparatus 189 

66.  Portable  Substations 194 

Problems 197 

CHAPTER  IX. 
TRANSMISSION  LINES. 

67.  Location  of  the  Transmission  Line 199 

68.  Number  of  Phases 201 

69.  Frequency 203 

70.  Economic  Voltage 205 

71.  Numerical  Illustration 211 


X  CONTENTS. 

ART.  PAGE 

72.  Separation  of  Conductors 213 

73.  Resistance  of  Conductors 220 

74.  Line  Inductance 222 

75.  Hyperbolic  Functions 224 

76.  Line  Capacity 230 

77.  Equations  of  Wave  Propagation  along  "Wires 235 

78.  Attenuation  and  Wave-length  Coefficients 238 

79.  Current  and  Voltage  Distribution  on  Lines 240 

80.  Regulation 243 

81.  Numerical  Illustration 244 

82.  Corona  Loss 247 

83.  Lightning 252 

84.  Protection  from  Lightning 254 

Problems 257 

CHAPTER  X. 

POWER  STATIONS. 

85.  Station  Load  Curves 259 

86.  Selection  of  Generators 261 

87.  Types  of  Prime  Movers 263 

88.  Power  Station  Costs 264 

Steam  Stations. 

89.  Engines  and  Turbines 265 

90.  Condensers 267 

91.  Boilers 270 

92.  Feed-water  Heaters 272 

93.  Chimneys  or  Stacks 272 

94.  Buildings 274 

95.  Arrangement  of  Apparatus 275 

96.  Cost  of  Steam  Stations 280 

97.  Operating  Expenses 280 

Hydraulic  Stations. 

98.  Turbines 281 

99.  Water-power  Development 288 

100.  Cost  of  Development 293 

101.  Depreciation  and  Obsolescence 297 

102.  Relative  Operating  Expenses 299 

103.  Costs  per  Kilowatt-hour 299 

Problems  . ,                                              3°* 


ELECTRIC   TRACTION   AND    TRANSMISSION 
ENGINEERING. 


CHAPTER  I. 

DETERMINATION   OF  THE   NUMBER  AND   SIZE   OF   CARS 
FOR  AN  URBAN  ROAD. 

1.  The    Engineer's    Problem.  —  The    problem    of    the 
electric  railway  engineer  is  the  determination  of  the  car 
equipment  required  to  yield  a  proposed  service,  the  char- 
acteristics of   the  low-potential  distribution   system,   the 
location  and  capacity  of  the  substation  equipment,  the 
characteristics  of  the  high-tension  transmission  line,  and 
finally  the  capacity  of  the  main  generating  station.     His 
report  should  include  cost  estimates  of  the  various  items 
of  the  electric  railway  system,  probable  operating  expenses 
and  approximate  gross  income  on  the  investment. 

2.  Types  of  Service.  —  The  object  of  a  railway  is  the 
transportation  of  passengers  or  freight  between  any  points 
on  the  road  in  accordance  with  a  schedule  which  is  pre- 
pared to  accommodate  the  traffic  most  economically  and 
to  lead  to  a  sufficient  income  on  the  original  investment 
to  the  operating  company.     The  probable  location  of  a 
proposed  electric  railway  is  governed  by  purely  local  con- 
ditions, such  as  density  of  population,  future  growth  of 
the  community,  and  topography  of  the  land.     An  approxi- 


N  :  AND « TRANSMISSION. 


mate  estimate  of  the  length  of  a  proposed  railway  and  its 
subsequent  income,  as  well  as  the  determination  of  the 
number  and  size  of  the  cars  or  trains,  may  be  obtained 
from  government  reports  and  other  statistical  sources. 

Electric  railway  undertakings  are  of  three  kinds,  —  new 
roads,  extensions  to  existing  railways,  and  electrifications 
of  present  steam  railroads.  Of  these,  the  former  will  first 
be  considered.  A  new  electric  railway  undertaking  may 
relate  to  an  urban,  suburban,  or  interurban  installation. 
Frequently  a  single  system  will  include  all  of  these  types 
of  service. 

3.  Length  of  Track.  —  For  a  new  urban  street  railway 
the  economically  feasible  length  of  road  will  depend  largely 
upon  the  population.  Thus,  curve  i  of  Fig.  i  shows  the 
number  of  miles  of  track  per  1000  of  population  for  various 
population  centers.  This  curve  represents  the  data  of  the 
following  table  showing  the  relation  of  trackage  and  traffic 
to  population  in  groups  of  urban  centers;  it  is  taken  from 
the  Census  Report  on  Electric  Railways  for  1902.  The 
figures  refer  to  single  track,  and  for  a  double-track  road  the 
length  of  track  is  twice  the  length  of  the  road. 


All  centers 
over  500,000 
population. 

All  centers 
between  100,000 
and  500,000 
population. 

Twenty-nine 
selected  centers 
between  25,000 
and  100,000 
population. 

Forty-six 
selected 
centers  of 
less  than 
25,000 
population. 

Total  population 
served  

10,274,470 

5,380,647 

1,258,615 

718,254 

Number  of  miles  of 
track 

4,008.80 

3,^0.82 

QCI.Q2 

48  c  oc 

Miles  of  track  per 
1000  of  population 
Number  of  passen- 
gers 

•49 
2,456,542,270 

.66 
004.327.853 

.76 

1^.842,312 

.68 
40,179,405 

Number    of    rides 
per  inhabitant  .  .  . 

239.1 

184.7 

107.9 

68.5 

NUMBER  AND   SIZE  OF   CARS   FOR  URBAN   ROAD.        ,3 


The  present  population  is,  however,  not  the  value  to  be 
considered  in  determining  the  track  factor,  T,  from  this 
curve,  but  instead  the  population  at  some  future  time, 
this  time  depending  upon  the  probable  duration  of  the 


.9 


.8 


.7 


o 

0.3 

O 

o 

a: 


.5 


0-4 


.3 


300 


240 


200 


160 


120  z 


80 


40 


0.25 


0.50 


1.00 


1.25 


1.50 


0.75 

MILLIONS 

AVERAGE    POPULATION. 

Fig.  i. 

period  of  construction,  the  depreciation,  and  later  pro- 
spective developments  in  electric  traction.  The  popula- 
tion, N,  at  some  future  time  may  be  estimated  from  the 
past  growth  of  the  community.  Thus,  a  curve  of  popula- 
tion for  the  last  one  hundred  years  might  be  drawn  and 


4  TRACTION   AND   TRANSMISSION. 

extended,  or  a  percentage  increase  of  population  may  be 
assumed.  A  population  value  corresponding  to  a  time 
ten  years  later  offers  a  reasonable  working  basis.  Then 
the  number  of  miles  of  track,  L,  to  be  installed  can  be 
expressed  as 

T  NT       ., 

L  = miles. 

1000 

4.  Receipts.  —  In  the  foregoing  table  is  also  given  the 
annual  number  of  rides  per  inhabitant  for  various  popu- 
lation centers,  the  data  showing  that  passenger  traffic  is 
comparatively   greater   in   the   larger   cities.     The   riding 
habit  of  people  increases  from  year  to  year  as  the  com- 
munity grows,  as  its  business,  family  and  social  life   be- 
comes more  complex,  and  as  its  facilities  for  intercommun- 
ication improve.     Curve  2,  Fig.  i,  shows  the  number  of 
yearly  passengers  per  inhabitant,  or  what  may  be  termed 
the  passenger  factor,  7.     Then  the  number  of  passengers 
per  year  can  be  written  as 

Yearly  passengers  =  Ny. 

The  annual  receipts,  in  dollars,  R,  of  a  traction  company 
are  evidently  the  product  of  the  total  yearly  passengers 
into  the  fare,  /,  in  dollars,  or 

R  =Nyf  dollars. 

In  this  country  the  usual  urban  fare  is  five  cents  regardless 
of  the  distance  traveled.  For  interurban  roads  the  fare 
depends  upon  the  distance  traveled,  varying  from  one  to 
three  cents  per  mile. 

5.  Number  of  Cars.  —  The  determination  of  the  num- 
ber of  cars  to  install  may  be  made  by  the  aid  of  tables 
which  show  the  income  and  operating  expenses  per  car 


NUMBER  AND   SIZE   OF   CARS   FOR   URBAN  ROAD.        5 


mile  of  a  number  of  electric  railways.  The  following  table 
compiled  by  H.  M.  Beardsley  gives  such  data  for  some 
electric  railways  in  New  York  State  for  1905.  Herefrom 
the  average  income  per  car  mile  is  21.56  cents. 


Company. 

Income  from 
operation. 

Income  per 
car  mile. 

Total 
expense  per 
car  mile. 

Albany  &  Hudson  

$200,671.65 

Cents. 
28  so 

Cents. 
24    3O 

United  Traction  Co.  of  Albany  .... 
Auburn  and  Syracuse  Co  

1,714,848.82 
268,507.78 

22-35 
2^.12 

15-35 
l6    24 

Binghamton  Ry.  Co  
International  Tr.  Co.  of  Buffalo  .  .  . 
Rochester  &  Eastern  

258,819.85 
3»6Q4»339  -oi 

212,668.51 

2O.  14 
25.16 

27.88 

11.23 
14.90 
21  .  ^6 

Cortland  Traction  Co 

40,130  86 

22    QZ 

16  06 

E.  W.,  L.  &  R.R.  Co.,  Elmira  
City  Ry.,  L.  &  R.-Co.,  Fishkill.  .  .  . 
Dunkirk  &  Fredonia 

192,921.47 
4i,474-56 

44,40   88 

16.06 

24.17 
26    02 

II  .61 

16.34 

22    C.7 

Hudson  Valley  Ry.  Co.,  Glens  Falls. 
Hornell  Elec.  Ry.,  Hornellsville.  .  . 
Ithaca  St.  Ry.  Co.,  Ithaca  
King.  Consol.  R.R.  Co.,  Kingston.. 
Orange  County  Trac.    Co.,   New- 
burgh  

499,148.09 
16,919.70 
91,817.90 
123,632.92 

119,270.85 

25-89 
9-30 
23.21 
23.08 

2O.O4 

18.13 
9.06 
17.87 
14-57 

1C  .  2Q 

Ogdensburg  St.  Ry.  Co  
I.  C.  &  R.  S.  Ry.  Co.,  Oneonta  

27,240.09 
103,862.05 

9.78 
15-97 

7.86 
13.82 

The  following  table  presents  information  compiled  by 
G.  H.  Davis  and  furnished  by  sixteen  electric  railway 
companies  which  represent  both  geographically  and  politi- 
cally nearly  all  sections  of  the  United  States  and  all  con- 
ditions of  operation.  The  values  given  are  for  the  year 
1910;  the  average  passenger  earnings  per  car  mile  being 
27.31  cents. 

The  growth  of  traction  earnings  in  the  larger  American 
cities,  together  with  the  corresponding  operating  expenses 
on  a  car  mileage  basis  are  shown  in  Fig.  2,  which  was  pre- 
pared by  B.  J.  Arnold.  It  will  be  noted,  for  instance,  that 
in  Brooklyn  the  earnings  per  car  mile  (average  for  street 


TRACTION   AND   TRANSMISSION. 


Company. 

Population  served 
within  corporate 
limits. 

*3 

|1 

Length  of  single 
track  in  miles. 

Car  miles  operated 
annually. 

Passenger  earnings 
per  car  mile  in 
cents. 

<l>  wT  ta 

||| 

I 

4.8?   2 

62 

27  80 

*        x 

20  o 

2 

3 

533,905 
465,786 

1,018,463 

585-0 
208.2 

37,537,433 

28-77 

4-34 
3  .  3 

14.4 
13.5 

4 

6 

7 
8 

9 
10 
ii 

373,740 
347,469 
516,152 
233,650 
131,105 
129,867 
155,000 
88,926 

403,740 
512,886 
516,152 
234,650 
151,105 
216,867 
185,000 

136.0 
IOI.7 
306.6 

139-7 
II0.4 
86.8 
186.0 

120  4 

13,812,813 
*i5,377,ooo 
24,229,010 
9,346,183 
6,895,421 
4,068,502 
9,538,867 

27.42 
3!-5o 
30.75 
28.86 
26.14 
28.70 
23.84 

26     14 

3.12 
3-62 
3-89 
*3-3 
4.09 
4.10 
4.09 

4    QO 

12.  I 
14.6 
17.7 
12.6 

16.1 

8-3 
18.0 
14  o 

12 

51,521 

60,521 

58  o 

7  8 

13 
14 
15 

16 

132,685 
36,346 
1,549,008 
46,000 

140,000 
71,346 
1,993,400 
46,500 

41.6 
627.6 

33-o 

6,194,583 
2,045,703 

70,943,404 
1,790,722 

26.32 
23-29 

25-34 
27.42 

4.08 
*4.2 

4-15 
4.07 

13-6 
9-5 
19-5 
8.8 

*  Estimated. 

and  elevated  railway  service)  increased  from  24  cents  in 
1902  to  29  cents  in  1906  and  then  decreased  to  26.8  cents 
in  1910. 

The  total  number  of  annual  car  miles  to  be  operated  is 
equal  to  the  annual  receipts  divided  by  the  annual  income 
per  car  mile  Rcm',  this  result,  when  divided  by  365  days 
and  the  daily  number  of  hours  of  operation,  h,  gives  the 
number  of  car  miles  to  be  operated  per  hour.  If  this  be 
divided  by  the  schedule  speed,  F,  in  miles  per  hour  includ- 
ing stops,  there  results  the  number  of  cars  required  for  the 
service.  The  schedule  speed  is  limited  by  city  ordinance 
in  many  cities  to  12  miles  per  hour  or  less.  The  smallest 
number,  v,  of  cars  required  then,  may  be  expressed  as 

R 

v  = 


NUMBER  AND   SIZE  OF  CARS  FOR  URBAN  ROAD. 


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8  TRACTION  AND  TRANSMISSION. 

6.  Size  of  Cars.  —  The  number  of  passengers  carried 
per  year  divided  by  365  and  the  number  of  cars  in  service 
gives  the  average  number  of  passengers  conveyed  by  each 
car  per  day.  The  number  of  trips  per  day  made  by  each 
car  is  found  by  multiplying  the  schedule  speed  by  the 
number  of  hours  the  car  operates  daily  and  dividing  by  the 
length  of  the  line.  The  average  number  of  passengers  per 
trip  is  therefore  p  =  NyL  =  NrRem 

365  vVh       1000  / 

When  several  lines  are  operated  in  the  same  district  or 
city,  the  second  member  of  this  equation  applies  to  each 
line  of  track-length  L  miles.  With  a  single  line  the  last 
member  is  applicable. 

The  number  of  passengers  riding  in  a  car  at  different 
times  varies  widely,  and  it  would  be  poor  economy  to  em- 
ploy cars  or  trains  of  such  size  as  to  permit  the  average  num- 
ber of  passengers  per  trip,  as  obtained  from  the  foregoing 
expression,  to  be  seated  at  one  time.  Not  all  of  these  passen- 
gers ride  the  full  length  of  the  road,  and  again,  others  may 
stand.  In  a  specific  case  information  should  be  obtained, 
from  records  concerning  similar  cases,  as  to  the  average 
length  of  fides  by  passengers.  Available  data  indicate  that 
the  average  passenger  ride,  r,  is  from  2  miles  to  4.5  miles. 

The  length  of  track  divided  by  the  average  length  of 
ride  determines  the  number  of  times  that  the  car  is  refilled 
each  trip.  The  average  number  of  passengers  per  trip 
divided  by  this  number  gives  the  passenger  capacity  of  a 
car  as  r  =  Nyr 

'' 


L  "365*7* 

an  expression  which  assumes  uniform  traffic  conditions. 
With  due   consideration  for  the  provision   of  additional 


NUMBER  AND   SIZE  OF   CARS   FOR   URBAN   ROAD. 


Fig-  3- 


Fig.  4. 


seats  for  the  accommodation  of  passengers  during  the  rush 
hours,  the  seating  capacity  of  the  car  is  thus  determined. 

Climatic  conditions  and  limitations  as  to  the  total  amount 
of  rolling  stock  determine  the  characteristics  of  car-body 


IO 


TRACTION  AND   TRANSMISSION. 


construction  as  to  whether  it  shall  be  open,  closed,  con- 
vertible, semiconvertible,  double-decked,  or  combination 
open  and  closed.  Figs.  3,  4,  5  and  6  show  the  Character- 


.  5- 


Fig.  6. 

istic  forms  of  construction  of  convertible,  "  Narragansett " 
open,  semiconvertible  interurban,  and  pay-as-you-enter 
closed  cars  respectively.  The  last  is  being  extensively 
adopted  for  congested  urban  traffic  because  it  facilitates 


NUMBER    AND    SIZE   OF   CARS   FOR   URBAN   ROAD.      II 

comfort,  ingress  and  egress  of  passengers,  and  collection 
and  conservation  of  fares. 

The  arrangement  of  seats,  as  to  whether  they  shall  be 
transverse,  longitudinal,  or  partly  both,  is  dictated  by  the 
type  of  service  to  be  rendered.  Transverse  seats  are  far 
more  comfortable  for  seated  passengers  and  are  essential 
in  long-haul  service.  Longitudinal  seats  greatly  facilitate 
ingress  and  egress  of  passengers,  give  greater  comfort  to 
standing  passengers,  and  as  a  rule  permit  of  a  greater  ratio 
of  standing  to  ( sea  ted  passengers.  In  urban  and  frequent- 
stop  service  facility  of  ingress  and  egress  is  of  paramount 
importance  in  order  that  a  high  schedule  speed  may  be 
maintained.  During  the  morning  and  evening  rush  hours 
the  number  of  standing  passengers  frequently  equals  that 
of  those  seated. 

The  weights  of  car  bodies  are  always  much  greater  than 
might  be  desired,  but  are  necessitated  in  order  to  give 
adequate  strength  to  withstand  the  rough  usage  of  ordi- 
nary service  and  to  give  some  insurance  against  collapse 
in  case  of  collision.  As  will  appear  later,  the  first  cost  and 
expense  of  operation  are  dependent  upon  the  total  weight. 
The  weight  of  passengers  seldom  reaches  one-quarter  the 
total  weight.  It  is  evidently  desirable  to  reduce  the  weight 
of  cars  to  a  minimum  consistent  with  adequate  strength. 

The  total  weights  of  closed  and  semiconvertible  cars  of  re- 
cent design  are  usually  between  90  and  130  poundsper  square 
foot  of  floor  area,  considering  the  floor  area  as  the  product 
of  the  length  over  bumpers  by  the  width  over  belt  rails. 

An  analysis  of  the  possible  saving  incident  to  the  use  of 
light  cars  in  a  group  of  street  railway  properties,  having 
for  1910  gross  earnings  of  approximately  $5,700,000,  shows 
that  of  the  92.33  per  cent  of  such  earnings  expended  for 


12 


TRACTION  AND   TRANSMISSION. 


all  purposes,  excluding  dividends,  including  operating  ex- 
penses 54.47  per  cent,  interest  24.74  per  cent,  taxes  7.12 
per  cent,  depreciation  6  per  cent,  only  53.08  per  cent  is 
influenced  by  car  weight  or  live  weight  transported.  Of 
this  the  items  particularly  affected  are  cost  of  power,  car 
and  track  repairs,  interest  and  depreciation,  which  in  the 
aggregate  do  not  generally  exceed  15  per  cent  of  the  gross 
earnings. 

Having  decided  upon  the  seating  capacity  of  the  car,  its 
size  and  weight  may  be  determined  from  the  following 
table.  The  average  weight  of  a  passenger  may  be  taken 
as  140  pounds.  The  weights  of  trucks  as  given  include 
the  weights  of  motors  except  where  starred. 

CAR   DATA. 


Type. 

Length  of 
body. 

Seating 
capacity. 

Weight  of 
body, 
pounds. 

Weight  of 
trucks, 
pounds. 

Closed  cars: 
Single  truck  
Single  truck  . 

16' 
18' 

22 
24 

6,000 

6.C7C 

4,600* 

4.  82C. 

Single  truck   . 

20'     8" 

32 

I3.7CO 

r  .12=? 

Single  motor  
Double  truck 

28' 
30'     8" 

38 

44 

11,310 

26,  72$ 

7,050 
14,500 

Manhattan  Elev  
I.R.  T.  Co.  (steel).. 
N.Y.  C.    (steel)  
Open  cars: 
8-bench 

/ 
42' 

44' 
50' 

15'     8" 

58 
60 
70 

32 

22,OOO 
56,300 
85,IOO 

6,37^, 

15,000* 
21,000* 
21,000* 

c.i  co 

lo-bench 

21' 

CQ 

13,340 

£,Q2< 

i2-bench     .    .    . 

30'     2" 

60 

1C,,  2  SO 

11,250 

i4-bench     .    .    . 

30'     2" 

7° 

20,300 

7,  ceo 

Semiconvertible  cars: 
Single  truck  
Single  truck  
Double  truck  

18' 
20'     8" 
28' 

24 
32 
40 

6,640 
10,240 
15,120 

4,900 
5,100 
10,450 

Double  truck  

30'     8" 

44 

IQXOO 

10,800 

7.   Numerical   Example.  —  As  a   numerical  example  of 
the  foregoing  method  of  estimating  the  number  and  size 


NUMBER  AND   SIZE   OF   CARS   FOR   URBAN   ROAD.      13 

of  cars  on  a  proposed  electric  railway  consider  the  case  of 
a  city  of  60,000  inhabitants  and  not  having  any  street  rail- 
way service.  Allow  a  25  %  increase  in  population  for  the 
subsequent  10  years.  The  economically  feasible  length 
of  track  is  o. 76  X  60  X  1.25  =  57  miles.  The  annual  re- 
ceipts of  the  operating  company  would  be  60,000  X  1.25  X 
132  X  .05  =  $495,000.  The  number  of  cars  required  is 

405,000  ,  .  , 

^^ =  24,  which  assumes  continuous  oper- 

.24  X  365  X  24  X  10 

ation  at  a  schedule  speed  of  10  miles  per  hour  and  an  income 

of  24  cents  per  car  mile.     The  number  of  passengers  per 

60,000  X  1.25  X  132  X  57  =  26g      Taki  irfte 

365  X  24  X  10  X  24 
as  the  average  passenger  ride,  the  capacity  of  the  car  with 

uniform  traffic  should  be  -    — —  =  21  passengers.    A  car 

having  a  seating  capacity  of  i^  times  this  number  of  pas- 
sengers, say  32,  would  be  appropriate  for  the  service. 
According  to  the  foregoing  table  such  cars  would  weigh 
with  live  load  23,355  pounds  or  n.68  tons. 

For  an  interurban  road  the  procedure  just  outlined 
would  be  modified  by  other  conditions,  such  as  the  dis- 
tance between  terminals,  the  ability  to  compete  with 
existing  steam  roads  in  regard  to  service,  the  schedule 
speed,  and  the  headway.  On  suburban  sections  the  sched- 
ule speed  is  most  frequently  from  15  to  20  miles  per  hour 
and  on  interurban  sections  from  25  to  35  miles  per  hour. 
The  highest  schedule  speed  at  present  for  limited  interurban 
service  is  55  miles  per  hour  on  a  36-mile  run.  At  high 
speeds  the  energy  consumption  per  mile  per  ton  of  car 
weight  is  much  greater  for  a  single  car  than  for  a  train  of 
several  cars,  and  consequently  economical  interurban  opera- 


14  TRACTION  AND   TRANSMISSION. 

tion  dictates  the  employment  of  trains  of  several  units  in- 
stead of  single  cars.  It  is  interesting  to  note  that  the  traffic 
on  an  interurban  railway  is  furnished  principally  by  the 
inhabitants  of  the  towns,  the  rural  districts  supplying  only 
from  about  20  to  30  %  of  the  total  traffic. 

PROBLEMS. 

1.  How  many  and  what  sized  cars  should  be  used  for  a  proposed  elec- 
tric railway  for  a  city  of  the  size  of  Portland,  Ore.?     The  schedule  speed  is 
specified  at  10  miles  per  hour  over  three  parallel  lines  of  equal  length,  the 
period  of  operation  to  extend  over  the  entire  day.     Take  4  miles  as  the 
average  passenger  ride  in  determining  car  capacity  for  uniform  traffic,  and 
provide  50%  additional  seats  for  the  accommodation  of  rush-hour  crowds. 
The  past  growth  of  this  city  is  indicated  below: 

1850 2,000  inhabitants 

1860 4,000 

1870 8,000 

1880 17,000 

1890 * 42,000 

1900 90,000 

1910 200,000 

2.  Plot  a  curve  showing  the  relation  which  should  exist  between  the 
population  of  the  city  just  referred  to  in  former  years,  and  the  seating 
capacity  serving  it  at  those  times. 


TRACTIVE   EFFORT   REQUIRED    FOR   CAR   PROPULSION.     15 


CHAPTER  II. 
TRACTIVE  EFFORT  REQUIRED  FOR   CAR  PROPULSION. 

8.  Train  Resistance.  —  The  determination  of  motor 
capacity  for  Ja  proposed  service  involves  a  knowledge  of 
the  tractive  effort  to  be  exerted  to  produce  the  specified  or 
assumed  acceleration  against  the  resistances  offered  by 
windage,  friction,  grades  and  curves,  and  also  information 
about  the  performance  of  various  sized  motors  such  as  is 
usually  embodied  in  motor  characteristic  curves  supplied 
by  the  manufacturers.  The  tractive  effort,  or  force  exerted 
at  the  rim  of  the  car  wheels,  required  to  propel  a  car  at 
constant  speed  on  a  straight  level  track  is  only  that  neces- 
sary to  neutralize  at  that  speed  the  resistance  offered  to 
car  movement  by  bearing  friction,  rolling  friction  and 
flange  friction  on  the  track,  and  wind  pressure;  these 
resistances  are  considered  under  the  single  term  train 
resistance.  Many  empirical  formulae  based  upon  experi- 
mental data  have  been  proposed  for  use  in  estimating  train 
resistance.  A  consideration  of  the  various  components  of 
train  resistance  mentioned  above  will  lead  to  the  formu- 
lation of  a  fairly  reliable  expression  therefor. 

Bearing  friction,  resulting  from  the  sliding  of  the  sur- 
faces of  the  axles  over  those  of  the  journals,  follows  the 
ordinary  laws  of  sliding  friction.  It  depends  upon  the 
pressure  between  the  surfaces,  and  increases  slightly  with 
speed.  Rolling  friction  is  due  to  deformation  of  the  rails 
and  wheel  rims  where  they  come  in  contact,  and  to  un- 


16  TRACTION   AND   TRANSMISSION. 

evennesses  in  the  surface  of  the  track.  The  energy  con- 
sumed in  overcoming  rolling  friction  is  theoretically  pro- 
portional to  the  weight  on  the  track  and  to  the  distance 
covered.  The  force  required  to  overcome  it  should  there- 
fore be  constant.  It  is,  however,  generally  assumed  to 
increase  slightly  with  the  velocity  of  the  train.  Experi- 
mental data  thus  far  obtained  warrant  the  following 
expression  for  the  tractive  effort  necessary  to  overcome 
bearing  and  rolling  friction: 

R'  =  k  +  KV, 

where  Rf  is  expressed  in  pounds  tractive  effort  per  ton  of 
car  weight,  V  is  the  speed  in  miles  per  hour,  and  k  and  K 
are  constants.  The  value  of  k,  since  it  depends  upon  the 
weight  concentrated  on  the  bearings,  may  be  expressed  in 
terms  of  train  weight,  W,  in  tons,  and  the  expression 


Vw 

gives  results  agreeing  well  with  experimental  values,  the 
minimum  value  of  k  being  limited  to  3.5.  Values  of  K 
obtained  experimentally  vary  from  0.03  to  0.07  depending 
upon  track  conditions  and  type  of  equipment,  the  lower 
values  being  the  more  representative.  For  light  equipment 
and  poor  conditions  of  track  the  use  of  higher  values  is 
desirable.  The  resulting  expression  for  bearing  and  roll- 
ing friction  may  then  be  written  simply  as 

lilll  *-ffi=+^. 

Vw    25 

The  principal  component  of  train  resistance  at  high 
speeds  is  the  wind  pressure  on  the  moving  car.  Wind 
pressure  varies  approximately  as  the  square  of  the  car 


TRACTIVE   EFFORT   REQUIRED    FOR   CAR   PROPULSION.    17 


velocity,  as  shown  by  numerous  experiments.  Therefore 
an  expression  for  head-end  wind  resistance  takes  the  form 

R"  =  k'SV2, 

where  S  is  the  car  cross  section  in  square  feet  and  kf  is  a 
constant  denoting  the  wind  pressure  per  square  foot  at 
unit  speed,  the  value  of  which  depends  upon  the  shape 
of  the  car  end.  For  cars  with  perfectly  flat  ends  its  value 
would  be  about  0.004  and  for  cars  of  the  pointed-nose 
design  kf  is  as  low  as  0.0015,  whereas  for  city  and  suburban 
cars  of  the  usual  types  and  for  the  modern  electric  locomo- 
tives a  value  of  0.0025  mav  De  taken  with  propriety.  The 
wind  pressure  thus  far  considered  is  that  on  the  car  end, 
but  there  is  also  air  resistance  at  the  sides  of  the  car  or 
cars,  which  effect  is  particularly  prominent  in  trains  of 
several  cars.  There  it  becomes  necessary  to  introduce  a 
factor  which  takes  care  of  this  skin  friction  along  the 
surface  of  succeeding  cars,  and  it  is  usual  to  add  10  %  of 
the  head-end  resistance  as  just  obtained  for  each  car  follow- 
ing the  first.  Then,  if  n  be  the  number  of  cars  in  the  train, 
the  tractive  effort  in  pounds  per  ton  of  train  weight  is 

zo        V        SV2  f        n  —  i~\ 

R  =  -^=  H 1 —  i  H pounds  per  ton, 

VPF      25      400  Wl  10   J 

a  formula  which  combines  the  various  expressions  of  the 
components  of  train  resistance.  Car  cross  sections  may 
be  taken  as  follows: 


Total  car  weight. 

S. 

20  tons 

go  sq.  ft. 

30     " 

TOO         " 

40     " 

no      " 

50     " 

120         " 

60 

1  2O         " 

i8 


TRACTION  AND   TRANSMISSION". 


Fig.  7  shows  by  curves  the  dependence  of  train  resis- 
tance upon  speed  and  weight  of  car  as  determined  by 
the  foregoing  formula. 

As  an  illustration,  determine  the  total  tractive  effort 
exerted  by  an  electric  car  (Berlin-Zossen  type)  when  run- 


40  60 

MILES  PER   HOUR. 

Fig.  7. 


80 


100 


ning  at  100  miles  per  hour  on  a  straight  level  track,  assum- 
ing the  weight  of  the  car  to  be  104  tons  and  the  cross- 
sectional  area  as  120  square  feet.  The  tractive  effort  per 

,     100    ,      I2o(lOo)2 

+  -   -  +  -  -  =  34.7  pounds,  and 

25       400  X  104 

the  total  tractive  effort  required  is  104X34.7  =3610  pounds. 


ton  is  R  = 


TRACTIVE   EFFORT  REQUIRED   FOR   CAR   PROPULSION.    19 


9.  Grades.  —  If  grades  be  encountered  additional  trac- 
tive effort  must  be  exerted.     If  a  car  be  on  a  grade  of 
inclination  a  to    the    hori- 
zontal plane,  Fig.  8,  the  com- 
ponent of  its  weight  along 

the  direction  of  motion  is 
W  sin  a,  the  Bother  compon- 
ent being  balanced  by  the 
reaction  of  .the  rails.  To 
maintain  uniform  motion 
up  the  grade  a  force  equal 
and  opposite  to  W  sin  a  must  be  exerted.  For  small  values 
of  a,  such  as  are  met  with  in  railway  work, 

sin  a  =  tan  a  approximately, 

and  therefore  grades  may  be  expressed  as  the  ratio  of  the 
vertical  rise  to  the  horizontal  length  of  grade.  It  is  cus- 
tomary, therefore,  to  consider  that  a  grade  of  q  per  cent 
means  a  rise  of  q  feet  in  a  hundred  feet.  The  tractive  effort 
necessary  to  propel  each  ton  of  car  weight  up  a  one  per 

cent  grade  is  therefore X  2000,  or  20  pounds,  and  to 

100 

draw  a  car  of  W  tons  up  a  grade  of  q  per  cent  with  uniform 
speed  requires 

G  =  20  qW  pounds 

tractive  effort.     For  a  down  grade  G  is  considered  negative. 

10.  Curves.  —  Curvature  of  track  presents  additional 
resistance  to  the  motion  of  a  car  because  of  increased 
flange  friction.     To  neutralize  this  effect  a  larger  tractive 
effort  must  be  exerted,  but  since  curves  are  usually  of 
short  length,  this  does  not  present  a  serious  factor.     Indeed 


20  TRACTION   AND  TRANSMISSION. 

track  curvature  may  be  ignored  in  calculations  of  required 
torque  unless  such  curves  are  numerous  and  very  sharp. 

Sharp  curves,  such  as  occur  with  city  traction  systems, 
are  generally  rated  by  radius,  but  long  curves  are  expressed 
in  degrees,  a  one-degree  curve  being  conventionally  denned 
as  one  in  which  a  chord  100  feet  long  will  subtend  an 
angle  of  one  degree  at  the  center.  Thus  the  radius  of  a 

one-degree  curve  is  quite  accurately  3  °  X  100^  ^          ^^ 

2  7T 

and  consequently  the  number  of  degrees  of  curvature,  c, 
of  a  curve,  specified  according  to  con- 
vention by  radius  R,  Fig.  9,  is 


c  =  ***-  degrees. 

Curve   resistance    is   usually  taken   as 
from  0.4  to  0.7  pound  per  ton  of  train 
weight  per  degree  of  curvature,  a  value 
Fig.  9.  Of  0.5  being  representative. 

When  a  car  moves  around  a  curve  it  experiences  a  cen- 
trifugal force  which  depends  in  magnitude  upon  the  speed 
and  mass  of  the  car,  and  the  degree  of  curvature.  This 
force  tends  to  derail  the  car  by  rotating  its  center  of  mass 
outwardly  around  the  outer  rail.  To  neutralize  this  ten- 
dency the  outer  rail  is  raised  above  the  inner  rail  to  such  an 
extent  that  the  plane  of  the  track  is  perpendicular  to  the 
resultant  of  the  centrifugal  and  gravitational  forces  acting 
on  the  car. 

Let      m  =  mass  of  car  in  pounds, 
v  =  speed  in  feet  per  second, 
g  =  acceleration  of  gravity  in  ft. /sec.2,  and 
R  =  radius  of  curve  in  feet. 


TRACTIVE  EFFORT  REQUIRED   FOR   CAR   PROPULSION.     21 


Then  — -  =  horizontal  centrifugal  force,  and 
K. 

mg   =  vertical  gravitational  force. 

An  inspection  of  Fig.  10  shows  that  the  resultant  of  these 
forces  will  be  perpendicular  to  the  plane  of  the  track  when 
that  plane  makes  an  angle  6 
with  the  horizontal  such  that 


A  road  section  devoid  of 
curves  is  said  to  have  a  tan- 
gent track. 

1 1 .  Acceleration.  —  In  the 

foregoing    paragraphs    only  Flgl  I0> 

the  torque  to  be  exerted  at  the  rim  of  the  car  wheels  for 
uniform  speed  was  determined.  But  in  railway  operation 
a  number  of  stops  must  be  made  to  allow  passengers  to 
board  or  alight  from  the  cars,  or  to  take  on  or  unload 
freight,  and  further,  between  these  stops  the  velocity  of 
the  car  must  be  such  as  to  maintain  the  specified  schedule. 
Thus  the  car  must  be  accelerated,  and  later  brought  to  rest. 
To  accelerate  a  car  requires  considerable  tractive  effort. 
The  force  in  pounds  acting  on  a  body  weighing  w  pounds 
which  produces  a  change  of  velocity  of  a  feet  per  second 
in  one  second  is 

—  a  pounds. 


Representing  the  weight  of  the  car  in  tons  by  W,  and  the 
rate  of  acceleration  in  miles  per  hour  per  second  by  A, 
then  the  tractive  effort  required  for  acceleration  alone  is 


22  TRACTION  AND   TRANSMISSION. 

,-,         2000  W          5280.4 

F  =  -    —  ••  -T  -  —  =  01.3  WA  pounds. 
32.2         60  X  60 

To  allow  for  the  energy  of  rotation  of  armatures,  wheels, 
etc.,  which  is  difficult  of  exact  determination  and  which 
depends  upon  the  construction  of  these  parts,  the  constant 
91.3  is  replaced  by  the  conservative  value  100.  Acceler- 
ation rates  of  from  \  mile  to  2  miles  per  hour  per  second  are 
usual.  The  greater  the  rate  of  acceleration  of  a  given 
equipment,  the  higher  will  be  the  schedule  speed  which 
can  be  maintained  thereby.  Limitations  are  imposed 
upon  the  maximum  acceleration  rate  attainable  by  con- 
siderations of  comfort  to  passengers,  permissible  starting 
current,  and  slipping  of  wheels  on  the  rails.  Thus  the 
total  tractive  effort  required  at  any  instant  for  the  pro- 
pulsion of  a  car  of  weight  W  tons  may  be  expressed  by  the 
complete  general  equation 

wv  .  SF2[     ,  w-il  ,  ,  We) 

h-    -|i  +  -        \  +  2oqW  +  - 

25  400   L  10   J  2     J 

+  TOO  WA  pounds. 

Representing  the  expression  in  braces,  which  includes  the 
effects  of  train  resistance,  curves,  and  grades,  by  Tt  pounds, 
and  rearranging,  the  acceleration 


100  W 

12.  Braking.  —  The  kinetic  energy  represented  by  a 
moving  car  at  any  instant  must  be  dissipated  in  some 
manner  if  the  car  is  to  be  brought  to  a  standstill  at  some 
later  time.  A  force  must  in  some  manner  be  exerted 
between  the  roadway  and  the  car,  and  must  be  in  such  a 
direction  as  to  oppose  and  retard  the  latter's  motion.  The 
force  generally  utilized  is  that  due  to  static  friction  between 


TRACTIVE   EFFORT   REQUIRED    FOR   CAR   PROPULSION.     23 

the  wheel  rims  and  the  track  rails  where  they  are  in  con- 
tact. Two  bodies  with  surfaces  held  in  contact  with 
each  other  by  transverse  pressure  are  capable  of  exerting 
forces  upon  each  other  along  the  direction  of  their  plane 
of  separation,  which  forces  may  be  varied  in  magnitude 
from  zero  to  such  a  maximum  as  will  initiate  slid- 
ing of  the  surfaces  with  respect  to  each  other.  This 
maximum  usually  bears  a  fairly  constant  ratio  to  the  trans- 
verse force  which  presses  the  surfaces  together,  and  is  the 
coefficient  of  friction  for  the  given  materials  of  which  the 
bodies  are  constituted.  This  coefficient  for  moving  steel 
wheel  rims  on  steel  rails  is,  however,  not  constant  because 
of  the  small  areas  in  contact  and  the  consequent  enormous 
normal  pressures,  and  because  fresh  surfaces  are  continu- 
ally becoming  effective.  This  variable  coefficient  is  also 
called  the  coefficient  of  adhesion,  and,  while  it  may  amount  to 
0.3  for  clean  dry  rails,  frequently  sinks  to  0.15  for  wet  rails, 
and  may  be  subsequently  raised  to  0.25  by  the  application 
of  sand.  If  the  maximum  retardation,  or  negative  acceler- 
ation, which  this  coefficient  0.25  will  permit,  be  represented 
by  AB,  then  the  maximum  retarding  force  or  braking  effort 

W 

FB  =  0.25  W  =  —  AB  tons, 

g 

and  consequently  the  retardation  rate 

AB  =  0.25  g  =  8.04  -~  =  5-5  miles  per  hour  per  second. 

To  bring  this  frictional  force  into  existence  the  kinetic 
energy  of  the  car  must  be  gradually  dissipated.  This  is 
usually  accomplished  by  pressing  brake  shoes  upon  the 
rims  of  the  wheels  so  that  the  energy  is  consumed  in  attri- 
tion and  heating  of  the  shoes.  The  pressure  on  the  brake 


24  TRACTION  AND   TRANSMISSION. 

shoes  is  attained  through  levers  actuated  by  hand,  by 
pneumatic  pressure,  or  by  electromagnetic  forces.  The 
energy  is  sometimes  allowed  to  expend  itself  in  rotating 
the  motor  shaft  against  an  electromagnetic  counter-torque, 
a  portion  of  the  energy  being  thus  returned  to  the  line. 

The  coefficient  of  friction  between  brake  shoes  and  wheel 
rims  decreases  with  increase  of  speed,  of  pressure,  and  of 
duration  of  application.  The  last  is  doubtless  occasioned 
by  the  local  elevation  of  temperature.  To  use  the  brake- 
shoe  friction  most  effectually  the  pressure  should,  there- 
fore, be  a  maximum  at  high  speed  and  be  reduced  with 
decreasing  speed.  This  friction  should  never  be  so  great 
as  to  cause  slipping  of  wheels  on  the  track,  for  the  adhesion 
is  thereby  reduced  and  flat  wheels  may  also  result. 

PROBLEMS. 

3.  Calculate  the  total  train  resistance  of  a  New  York  Central  locomotive 
weighing  220,000  pounds  when  it  runs  alone  at  a  uniform  velocity  of  a  mile 
per  minute.  Cross  section  of  locomotive  is  120  square  feet. 

4.  Determine  the  tractive  effort  required  to  enable  a  train  consisting  of 
5  motor  cars  and  3  trailers  to  climb  a  3.1  %  grade  with  a  uniform  speed  of 
15  miles  per  hour.     The  weight  of  the  trucks  per  car  is  9  tons;  the  weight 
of  motors  and  control  equipment  per  motor  car  is  7^  tons;  and  the  weight 
of  a  car  body  is  21  tons.     Each  car  can  accommodate  80  passengers  (aver- 
age weight  =  140  pounds). 

5.  If  a  curve  having  a  radius  of  1500  feet  existed  on  this  section  of 
the  road,  how  much  additional  tractive  effort  must  be  exerted  to  maintain 
the  same  velocity? 

6.  Calculate  the  total  tractive  effort  required  to  accelerate  a  car  weigh- 
ing 30  tons,  carrying  50  passengers,  at  the  rate  of  1.3  miles  per  hour  per 
second  on  a  tangent  level  track.     Take  140  pounds  as  the  average  weight 
of  a  passenger.     Neglect  train  resistance. 

7.  Assume  a  train  to  be  running  on  a  straight  level  track  at  60  miles  per 
hour  and  an  adhesion  of  0.25  to  be  available  for  making  an  emergency  stop. 
Find  the  elapsed  time  and  distance  covered  in  making  the  stop. 

8.  Determine  the  proper  elevation  of  the  outer  rail  of  a  track  for  train 
speeds  of  25  miles  per  hour  and  a  curvature  of  6  degrees. 


TYPES   AND    PERFORMANCE    CURVES   OF   MOTORS.       25 


CHAPTER  III. 

TYPES  AND  PERFORMANCE  CURVES  OF  MOTORS. 

13.  Traction  Motors.  —  An  electric  motor  suitable  for 
traction  purposes  must  exert  the  necessary  torque  for 
accelerating  the  car  at  the  predetermined  rate,  or  to  pro- 
pel the  car  up  a  grade,  without  causing  excessive  energy 
demands  from  the  central  station.  This  is  possible  only 
when  large  tractive  efforts  are  exerted  at  low  speeds,  which 
follows  from  the  fact  that  the  power  output  of  a  motor  is 
equal  to  the  product  of  torque  and  speed.  Torque  depends 
upon  the  field  flux  and  the  current  in  the  armature  of  the 
motor.  The  former  varies  with  the  field  current,  ancf,~in 
an  unsaturated  motor,  would  be  directly  proportional  to 
that  current,  but  in  practice  it  is  somewhat  less  than  this 
proportion  indicates.  The  speed  of  any  motor  depends 
upon  the  field  flux,  number  of  armature  conductors,  num- 
ber of  pairs  of  poles,  and  the  counter  electrom'otive  force 
generated  in  the  armature  ;  thus 

(E  -  IaRa)  60.  io8 


where  E  is  the  impressed  EM.  P.,  Ia  is  the  armature 
current  in  amperes,  Ra  is  the  armature  resistance  in  ohms, 
p  is  the  number  of  pairs  of  field  poles,  <1>  is  the  magnetic 
flux  per  pole  in  maxwells,  and  5  is  the  number  of  arm- 
ature conductors  in  series  between  brushes. 


26  TRACTION  AND   TRANSMISSION. 

14.  Direct-current  Motors.  —  In  a  series  direct-current 
motor  the  armature  and  field  windings  are  connected  in 
series  and  are  traversed  by  the  same  current ;  therefore  the 
torque  exerted  is  roughly  proportional  to  the  square  of 
that  current.  If  a  small  current  flows,  the  field  strength 
will  be  low,  and  from  the  foregoing  expression  for  speed  it- 
is  seen  that  the  speed  will  be  high.  Again,  if  the  motor 
takes  a  large  current,  the  field  strength  will  be  intense 
and  consequently  the  speed  will  be  low.  Thus,  a  series 
motor  exerting  large  torque  runs  at  low  speed,  and  when 
exerting  little  torque  operates  at  high  speed.  It  follows 
that  the  power  consumption  of  a  series  motor  does  not 
fluctuate  violently,  and  therefore  is  well  suited  for  rail- 
way work. 

In  the  shunt  direct-current  motor  the  field  strength  is 
approximately  constant,  and  therefore  the  torque  is  directly 
proportional  to  the  current  and  the  speed  is  practically 
constant.  When  a  large  torque  is  required  from  such  a 
motor  its  power  consumption  is  enormous,  since  the  speed 
is  not  materially  lowered.  Consequently  the  central  station 
supplying  equipment  of  this  kind  would  be  subject  to  great 
load  variations.  For  this  reason  shunt  motors  are  not  used 
on  railways. 

The  direct-current  series  motor  operating  at  500  or  600 
volts  has  been  in  use  since  the  advent  of  the  electric  railway. 
At  present  a  few  roads  employ  direct-current  series  motors 
operating  at  pressures  up  to  1400  volts.  Fig.  n  shows 
one  of  the  G.  £.-205,  i2oo-volt  commutating-pole  railway 
motors  used  on  the  Pittsburg-Newcastle  railway. 

The  tendency  being  to  reduce  the  initial  investment  of  a 
railway  system,  its  operation,  particularly  over  long  dis- 
tances, must  be  effected  at  high  voltages,  since  the  principal 


TYPES   AND    PERFORMANCE   CURVES   OF   MOTORS.      27 

item  of  expense  is  the  distributing  system  itself.  But  com- 
mutation difficulties  limit  the  voltage  of  direct-current 
railway  motors  to  about  1400  volts.  Therefore  it  is  usual 
to  generate  a  high  alternating  electromotive  force,  preferably 
three-phase,  at  the  power  house,  and  to  supply  alternating 
current  at  this  high  voltage  to  a  number  of  substations 
where,  by  means  of  transformers  and  converters,  this  cur- 
rent is  changed  to  direct  current,  which  is  then  supplied 


Fig.  ii. 

to  the  railway  motors  over  the  low-tension  distribution 
system.  Such  generation  and  transformation  entail  large 
initial  investment  and  operating  expenses,  and  also  con- 
siderable energy  loss.  These  items  may  be  greatly  reduced 
by  employing  alternating-current  motors,  which  can  be  oper- 
ated at  a  potential  of  several  thousand  volts. 

15.  Alternating-current  Motors.  —  The  advantages  in- 
cident to  the  use  of  the  alternating-current  motor  are 
the  lower  first  cost  of  the  low-tension  distribution  system, 


28  TRACTION  AND  TRANSMISSION. 

the  substitution  of  the  simple  and  efficient  transformer 
substation  for  the  converter  substation,  and  the  reduction 
of  the  cost  of  operation.  It  is  not  advisable  to  employ 
high  trolley  potentials  in  cities  or  densely  populated  sub- 
urban districts,  but  for  trunk  line  operation,  requiring 
an  infrequent  service,  economical  operation  dictates  high 
trolley  potentials;  in  many  cases  transformation  to  a  lower 
motor  voltage  is  effected  by  transformers  on  the  cars  or 
locomotives.  In  alternating-current  traction,  controller  sys- 
tems may  be  utilized  which  do  not  entail  the  large  energy 
losses  incident  to  starting  direct-current  motors. 

Three-phase  generation  is  more  economical  than  single- 
phase  generation  of  E.M.F.  The  current  from  the  former 
system  may  be  converted  into  a  two-phase  current  by  means 


8-PHASE  HIGH    TENSION 
TRANSMISSION  LINE. 


TROLLEYS 

Fig.  12. 


of  a  Scott  transformer,  each  phase  of  which  supplies  single- 
phase  current  to  the  motors  on  one  side  of  the  station. 
Fig.  12  shows  the  scheme  of  connections. 

There  are  several  types  of  alternating-current  single- 
phase  railway  motors  at  present  in  operation,  but  of  these 
the  compensated  series  motor  is  the  only  one  used  in  this 
country.  Repulsion  motors  are  used  abroad  to  a  consid- 
erable extent;  single-phase  induction  motors  starting  as 
repulsion  motors  have  not  been  seriously  considered  from 
the  railway  viewpoint. 


TYPES  AND   PERFORMANCE   CURVES  OF  MOTORS.      29 

Series  Mot6rs.  —  Consider  a  direct-current  armature 
mounted  within  a  single-phase  alternating  magnetic  field, 
as  in  Fig.  13.  When  the  armature  is  stationary  an  electro- 
motive force  will  be  induced  in  the  armature  turns,  due 
to  the  alternating  flux  which  passes  between  the  field 
poles.  The  greatest  E.M.F.'s  will  be  induced  in  the  turns 
perpendicular  to  the  field  axis,  since  these  turns  link  with 


Fig.  13. 

the  greatest  number  of  lines  of  force;  and  no  E.M.F.'s  will 
be  induced  in  the  turns  in  line  with  the  field  axis.  The 
directions  of  the  E.M.F.'s  induced  in  the  armature  turns 
by  the  change  in  field  flux  are  indicated  in  the  figure  by 
the  full  arrows,  and  it  is  seen  that  the  maximum  value  of 
this  E.M.F.  is  across  BC.  As  in  transformers,  the  effec- 
tive value  of  this  electromotive  force  is 

,.,         2  q/fr  JV 

ET  =  >  (!) 

V  2  I08 

where  <£m  is  the  maximum  value  of  the  flux  entering  the 


30  TRACTION  AND   TRANSMISSION. 

armature  and  N  is  the  equivalent  number  of  armature 
turns. 

The  maximum  number  of  lines  of  force  linked  with  a 
single  turn  depends  upon  the  position  of  this  turn  in  the 
magnetic  field,  and  is  proportional  to  the  greatest  value  of 
<J>m  times  the  cosine  of  the  angle  of  displacement  of  the 
turn  from  the  position  AD.  Assuming  the  turns  to  be 
evenly  distributed  over  the  periphery  of  the  armature,  the 
average  value  of  the  maximum  flux  linked  with  the  arma- 

ture turns  will  be  -  <£m.     If  there  be  Na  conductors  on  the 

7T 

armature,  the  number  of  turns  connected  in  continuous 

N 

series  will  be  -—  ••     The  electromotive  forces  induced  in 
2 

the  upper  and  lower  groups  of  armature  turns  are  added 
in  parallel,  consequently  the  effective  number  of  turns  in 

i    N       N 
series  is  -  •  -  -  =  —  -  -     Therefore  the  equivalent  number  of 

22  4 

armature  turns  may  be  expressed  as 

N  .  H  .  ?L  _  N*.  (2) 

7T          4  2  7T 

Substituting  this  value  of  N  in  equation  (i),  the  E.M.F. 
induced  in  the  armature  winding  by  the  change  in  value  of 
the  field  flux  is 


,v 

(3) 

I0 

and  it  lags  90°  behind  the  field  flux  in  time. 

If  the  brushes  of  the  motor,  A  and  D,  are  placed  at  the 
points  shown  in  Fig.  13,  this  electromotive  force  will  not 
manifest  itself  externally,  since  it  consists  of  two  equal 
and  opposite  components  directed  toward  these  brushes. 
This  E.M.F.  appears,  however,  in  the  coils  short-circuited 


TYPES  AND   PERFORMANCE   CURVES   OF  MOTORS.      31 

by  the  brushes,  as  will  be  shown  later.  The  current, 
which  enters  the  armature  by  way  of  the  brush  and  which 
traverses  the  two  halves  of  its  windings  in  parallel,  pro- 
duces an  armature  flux  of  maximum  value  $am.  This  sets 
up  a  reactance  E.M.F.  in  the  armature  which  in  the  case 
of  uniform  gap  reluctance  can  be  similarly  expressed  as 

(4) 

E0° 

and  lags  90°  behind  the  current. 

When  the  armature  revolves,  there  are,  in  addition, 
electromotive  forces  induced  in  the  armature  conductors  as 
a  result  of  their  cutting  the  field  flux.  The  directions  of 
these  E.M.F.'s  are  indicated  by  the  dotted  arrows,  and  it 
is  seen  that  these  E.M.F.'s,  generated  by  the  rotation  of 
the  armature,  add  to  each  other  and  appear  on  the  com- 
mutator as  a  maximum  across  AD. 

The  average  value  of  the  electromotive  force  due  to  the 
rotation  of  the  armature  in  a  bipolar  field  is 

Erotav  =  ^£-10-*, 
oo 

where  V  is  the  armature  speed  in  rev.  per  min.  and  <£/  is 
the  field  flux;  and  the  effective  value  of  this  E.M.F.  is 

*fmNa     V  M 

Erot  =   -J= '  —  >  (5) 

V  2  IO8      °° 

and  is  in  time  phase  with  the  field  flux,  but  appears  as  a 
counter  E.M.F.  at  the  brushes  AD. 

When  an  alternating  current  is  passed  through  the  field 
coils,  the  alternating  field  flux  is  set  up,  and  this  flux  pro- 
duces a  reactive  E.M.F.  in  the  field  winding  lagging  90° 
behind  the  flux  in  phase,  exactly  as  in  a  choke  coil.  The 
magnitude  of  this  E.M.F.  is 


TRACTION  AND   TRANSMISSION. 


**/  ~~ 


\/2I08 

is  the  maximum  value  of  the  field  flux,  and 


(6) 


where  <i>/ 

is  the  number  of  field  turns. 

The  electromotive  force,  E,  which  is  impressed  upon  the 
motor  terminals,  is  equal  and  opposite  to  the  vectorial 
sum  of  Ea,  Erot,  Ef,  and  the  IR  drop  of  the  armature  and 
field  windings,  as  shown  in  Fig.  14,  where  /  is  the  current 


IR 


E. 


Fig.  14. 

flowing  through  the  field  and  armature,  and  <£  represents 
the  phase  of  the  flux.  In  this  diagram,  eddy  current  and 
hysteresis  losses  are  ignored.  The  impressed  electromotive 
force  is  therefore 

E  =  V(Erot  +  IR)*  +  (Ea  +  Ef)\  (7) 

In  the  series  motor,  the  same  current  passes  through 
field  and  armature  windings,  and,  if  uniform  reluctance 
around  the  air  gap  be  assumed,  then  the  armature  and  field 
fluxes  will  be  proportional  to  the  equivalent  armature  turns 
and  field  turns  respectively.  Therefore 


f 
TYPES  AND   PERFORMANCE   CURVES  OF  MOTORS.      33 

*«.:*/.,  =  #:#/  =  —  :  Nf.  (8) 

2  7T 

Representing  the  ratio  of  the  field  turns  to  the  effective 

N 
armature    turns   by   T,    then   3>/m  =  T$am,  and  Nf  =  T—*' 

27T 

Therefore  expressions  (4)  and  (6)  become  respectively 


fbf    A7 
A  Z?  ^ffni'L  '  a          /• 

and  Ef  =  -^  —  -  •  fr. 

V  2  IO8 

Equation  (5)  then  reduces  to 

ETOt=\Ea--i  and  Erot=jEf--' 

f        OO  /r        OO 

Therefore  Es  =  r2Ea. 

Neglecting   the  armature   and  field   resistance   drop,   the 
impressed  E.M.F.  becomes 


which  is  the  fundamental  E.M.F.  equation  of  the  plain 
series  motor. 

The  power  factor  of  the  motor  is 

Erot  rV  f     ^ 


and  the  current  supplied  to  the  motor  is 


still  neglecting  the  motor  resistance. 


34  TRACTION  AND   TRANSMISSION. 

When  V  =  60 /,  the  motor  is  said  to  run  at  synchronous 
speed  (bipolar  field).     The  power  factor  of  a  plain  series 

motor,  having  r  =  i,  when  running  at  this  speed,  is  -—:> 

or  0.446,  and  for  values  of  r  other  than  unity  the  power 
factor  is  less  than  0.446.  It  is  true  that  if  the  resistance 
of  the  motor  be  considered,  the  power  factor  will  exceed 
this  value,  but  nevertheless  it  remains  extremely  low. 

7^ 

The  current  intake  under  these  same  conditions  is  — = 


When  the  motor  is  at  standstill,  V  =  o,  and  the  power 
factor  is  zero.  The  current  intake  at  standstill  is  — —  • 
Hence  the  ratio  of  the  current  at  synchronism  to  the  cur- 
rent at  standstill  is  —p  -r-  -  =  0.894.  The  ratio  of  the 
V  5  2 

torque  at  synchronous  speed  to  the  torque  at  standstill, 

/  i  \2 
since  it  varies  as  the  square  of  the  current,  is  (~~F-)  + 

-J   =  0.80,  which  shows  that  the  starting  torque  is  but 

little  greater  than  the  torque  at  synchronous  speed.  Since 
for  railway  service  motors  are  required  having  large  start- 
ing torque  and  which  torque  rapidly  decreases  as  the  speed 
of  the  motor  increases,  it  is  seen  that  independent  of  its 
low  power  factor,  the  plain  series  motor,  having  uniform 
magnetic  reluctance  around  the  air  gap,  is  unsuitable  for 
traction  and  for  similar  purposes. 

If,  however,  the  reluctance  of  the  air  gap  in  the  direction 
AD,  Fig.  13,  be  increased,  the  power  factor  and  speed- 
torque  characteristics  will  be  improved,  and  these  will 
depend  largely  upon  the  ratio  of  field  turns  to  effective 
armature  turns,  as  will  be  seen  by  considering  the  construe- 


TYPES  AND   PERFORMANCE   CURVES  OF  MOTORS.      35 

tion  of  the  motor  to  be  such  that  the  proportion,  equation 
(8),  must  be  modified  by  introducing  into  its  antecedents 
a  constant  considerably  greater  than  unity.  A  motor 
of  this  kind,  with  few  field  turns  compared  to  arma- 
ture turns,  might  be  suitable  for  traction,  but  more 
important  improvements  have  been  made,  which  will  now 
be  discussed. 

It  appears  from  Fig.  14  that  the  power  factor  of  series 
motors  may  be  increased  by  increasing  IR  and  Erot,  or  by 
decreasing  Ef  and  Ea.  It  is  obvious  that  increasing  IR 
signifies  an  increase  in  losses,  thus  resulting  in  a  lower 
efficiency.  Erot  can  be  increased  by  increasing  the  number 
of  armature  turns.  Both  Ef  and  Ea  can  be  decreased  by 
lowering  the  frequency  without  affecting  Erot,  hence  low 
frequencies  are  desirable.  To  decrease  the  reactive  elec- 
tromotive force  of  the  field,  it  is  necessary  that  the  reluc- 
tance of  the  magnetic  circuit  be  low,  i.e.,  small  air  gap  and 
low  flux  densities  in  the  iron,  in  order  that  the  required 
flux  can  be  produced  by  a  minimum  number  of  ampere- 
turns.  The  armature  reactive  E.M.F.,  Ea,  is  not  essential 
to  the  operation  of  the  motor,  and  can  be  neutralized  by 
the  use  of  compensating  windings,  and  this  feature  of 
alternating-current  series  motors  is  a  very  important  one. 

The  compensating  winding  is  embedded  in  slots  in  the 
pole  faces,  as  shown  in  Fig.  15,  which  represents  a  West- 
inghouse  four-pole  compensated  single-phase  railway  motor 
with  its  armature  and  field  windings  removed.  The  num- 
ber of  turns  of  the  compensating  winding  is  adjusted  so 
as  to  set  up  a  magnetomotive  force  equal  and  opposite  to 
that  due  to  the  current  in  the  armature  coils.  The  com- 
pensating winding  may  be  energized  either  by  the  main 
current,  by  placing  this  winding  in  series  with  field  and 


TRACTION  AND   TRANSMISSION 


armature,  or  by  an  induced  current,  which  is  obtained 
by  short-circuiting  the  compensating  winding  upon  itself, 
thus  utilizing  the  principle  of  the  transformer  in  that  the 
main  and  induced  currents  are  opposite  in  phase.  The 


Fig.   15. 


former  method  of  neutralizing  Ea  is  known  as  conductive 
or  forced  compensation,  and  may  be  used  with  both  alter- 
nating and  direct  currents,  and  the  latter  method  is  known 


Fig.  16. 


Fig.  17. 


as  inductive  compensation,  and  may  be  used  only  with  alter- 
nating current. 

Figs.  1 6  and  17  show  schematically  the  connections  of 
the  conductively  and  inductively  compensated  alternating- 
current  series  motors  respectively.  The  compensating 
winding  is  preferably  distributed  so  that  the  armature 


TYPES   AND    PERFORMANCE    CURVES   OF   MOTORS.      37 

reactance  is  neutralized  as  completely  as  possible.  The 
current  flows  in  the  same  direction  in  all  of  the  conductors 
of  the  compensating  winding  embedded  in  one  field  pole, 
and  flows  in  the  opposite  direction  in  the  conductors  em- 
bedded in  the  adjacent  poles. 

When  the  compensating  winding  completely  neutralizes 
the  armature  reactance,  the  impressed  electromotive  force 
from  equation  (7)  is 

.    E  =  V(Erot  +  IR)*  +  Ef\  (12) 

where  R  is  the  resistance  of  the  motor  including  that  of  the 
compensating  winding.  If  the  resistance,  R,  be  neglected, 
then,  since 

V 


the  impressed  electromotive  force  becomes 


V   \2 

77  T?    \  I  I       V       \    _|_  n 

£  =  £/Vi6-^J+I- 


and  therefore  the  power  factor  is 


E        VV2  +  (6o/r) 
The  motor  current  is 


At  synchronous  speed  V  =  60  /,  and  therefore  the  power 
factor  at  this  speed  becomes  - 

Vl+T2 

Still  neglecting  the  motor  resistance,  the  current  intake 

ET 

at  synchronous  speed  is  -  >  and  at  standstill  it 

Xf  Vi  +  r2 


TRACTION   AND   TRANSMISSION. 


is  — '  consequently  the  ratio  of  the  current  at  synchronous 


speed  to  the  current  at  standstill  is 


w+ 


Since  torque 


varies  as  the  square  of  the  current,  the  ratio  of  the  torque 

T2 

at  synchronous  speed   to   the  starting   torque  is   -     — -• 


Hence  it  follows  that  the  speed-torque  characteristics  of 
a  compensated  series  motor  may  be  adjusted  to  the  re- 
quired conditions  by  properly  proportioning  the  number  of 
armature  and  field  turns. 

Repulsion  Motors.  —  The  repulsion  motor  consists  of  a 
field  resembling  the  stator  of  the  single-phase  induction 
motor,  and  an  armature  which  is  similar  to  the  armatures 
of  direct-current  and  alternating-current  series  motors. 
The  armature  winding  always  remains  short-circuited  in 
a  line  inclined  at  a  definite  angle  with 
the  field  axis,  this  being  accomplished 
by  means  of  brushes,  bearing  on  the 
commutator,  which  are  joined  together 
by  a  conductor  of  low  resistance.  The 
field  winding  is  supplied  with  single- 
phase  alternating  current.  The  fact 
that  the  armature  and  field  windings 
are  electrically  distinct  makes  it  pos- 
sible to  operate  the  motor  on  high- 
voltage  systems,  the  armature  winding 
being  so  adjusted  that  the  currents 
therein  can  be  commutated  satisfac- 
torily. 

The  pulsating  flux  through  the  armature,  produced  by 
the  alternating  current  in  the  field  winding,  may  be  re- 


Fig.  18. 


TYPES  AND   PERFORMANCE   CURVES  OF  MOTORS. 


39 


solved  into  two  components,  one  in  the  direction  of  the 
brush  axis  and  the  other  perpendicular  thereto;  these 
being  represented  in  Fig.  18  respectively  by  OA  and  OB. 
The  component  OA  produces  an  EM. P.  in  the  armature 
conductors  and  causes  a  current  to  flow  through  them. 
The  other  component,  OB,  reacts  upon  this  armature 
current,  thereby  developing  torque. 

Induction  Motors. — The  three-phase   induction   motor 
may  be  used  for  traction  purposes  where  the  service  require- 


Fig.  19. 

ments  are  of  a  constant  nature,  such  as  on  long  mountain 
grades.  The  induction  motor  is  practically  a  constant- 
speed  motor,  the  speed  variation  being  less  than  about 
ten  per  cent  of  the  no-load  value/and  therefore  causes 
large  energy  demands  on  the  central  station.  On  the  other 
hand,  energy  may  be  returned  to  the  system  when  trains 
operated  by  them  descend  grades.  This  type  of  motor 
is  adapted  for  heavy  traction  with  infrequent  stops.  Two 
or  three  separate  trolleys  are  necessary  for  such  oper- 
ation. Fig.  19  shows  the  motors  and  the  method  of  their 
mountings  on  the  trucks  on  the  locomotives  used  in  the 


40 


TRACTION  AND  TRANSMISSION. 


Cascade  tunnel  of  the  Great  Northern  Railroad.  Six 
thousand  six  hundred  volts  are  delivered  to  the  locomotives 
from  two  trolley  wires  and  the  track  rails,  and  are  stepped 
down  by  transformers  in  the  cab  to  500  volts,  which  are 
impressed  upon  the  motor  terminals. 

1 6.  Methods  of  Drive.  —  Traction  motors  may  drive 
the  car  wheels  by  means  of  gears,  connecting  rods,  or 
driving  pins.  The  first  method  is  universally  employed 


Fig.  20. 

on  street  railways,  the  speed  being  reduced  by  a  pinion 
on  the  motor  shaft  meshing  with  a  gear  wheel  on  the  wheel 
shaft.  Fig.  20  shows  two  geared  G.  £-69,  200  horse- 
power direct-current  motors  mounted  upon  a  truck,  as 
used  on  the  West  Jersey  and  Seashore  Railroad.  The  latter 
methods  of  drive  are  used  in  high-speed  locomotive  service. 
In  the  Pennsylvania  electric  locomotives  the  motors  are 
mounted  upon  the  frame  and  side-connected  to  driving 
wheels  by  a  system  of  cranks  and  parallel  connecting  rods, 


TYPES  AND   PERFORMANCE   CURVES   OF  MOTORS.     41 


TRACTION  AND  TRANSMISSION. 


TYPES   AND    PERFORMANCE   CURVES   OF   MOTORS.     43 

similar  to  steam  practice.  Fig.  21  shows  a  truck  of  one  of 
these  locomotives  with  the  cabs  removed  so  as  to  show  the 
method  of  mounting  the  motors.  The  connecting  rods  and 
all  reciprocating  parts  are  counterbalanced  so  as  to  elimin- 
ate pounding  on  the  track.  In  the  New  Haven  locomotives 
the  motors  are  mounted  upon  a  quill  surrounding  the  driv- 
ing axle,  the  torque  being  transmitted  to  the  wheels  directly 
by  projecting  pins  on  the  armature  structure  engaging  in 
sockets  in  the  .spokes  of  the  driving  wheels.  Fig.  22  gives, 
at  the  top,  two  views  of  a  quill,  and  at  the  bottom,  two 
views  of  the  quill  in  place  upon  the  axle  before  the  motor  is 
mounted.  In  some  installations,  notably  in  the  New  York 
Central  locomotives,  the  motor  armatures  are  mounted  di- 
rectly on  the  driving  axle,  being  rigidly  connected  thereto. 
17.  Motor  Curves.  —  The  characteristic  curves  of  a 
motor  include  curves  of  speed,  torque,  and  efficiency  in 
terms  of  the  current  flowing  through  the  motor.  Instead 
of  using  the  speed  of  the  motor  in  revolutions  per  minute 
and  the  torque  in  pounds  at  one  foot  radius,  it  is  usual  in 
railway  practice  to  plot  the  speed  of  the  car  in  miles  per 
hour  and  tractive  effort  or  the  force  exerted  at  the  rim  of 
the  car  wheels  in  pounds.  The  relations  between  these 
quantities  are  given  by  the  following  equations,  where 

Vm  =  motor  speed  in  revolutions  per  minute, 

T  =  tractive  effort  in  pounds, 

ng  =  number  of  teeth  on  gear, 

np  =  number  of  teeth  on  pinion, 

D  =  diameter  of  car  wheel  in  inches, 

T'  =  motor  torque  in  pound-feet, 

V  =  speed  of  car  in  miles  per  hour,  and 

€g  =  gear  efficiency. 


44 


TRACTION   AND   TRANSMISSION. 


2000 


100 


120 


Fig.  23. 


TYPES  AND  PERFORMANCE   CURVES  OF   MOTORS     45 


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0                    75                   150                  225                 300                  375                  450                 52 
AMPERES 

Fig.  24. 

TRACTION   AND   TRANSMISSION. 


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1500 


1750 


TYPES  AND  PERFORMANCE  CURVES   OF  MOTORS.      47 


250  H  P.   MOTOR 

3000  VOLTS 


10 


20  30  40  50 

AMPERES  PER  PHASE 

Fig.  26. 


60  70 


48  TRACTION  AND   TRANSMISSION. 

The  work  performed  by  the  motor  while  its  armature 
makes  one  revolution  is  2  -n-T'.  When  multiplied  by  the 
gear  efficiency  it  also  represents  the  work  done  by  the  trac- 
tive effort  in  turning  the  car  wheel  through  the  correspond- 
ing portion,  np/ng,  of  a  revolution.  Therefore,  the  wheel 
radius  being  .D/24  feet, 

2ireaT/  =  2  TT  --  -  T  foot-pounds. 

24  na 

...    T  =  %L  j±eg  T'  pounds. 
Hp  D 

Equating  the  effective  power  exerted  by  the  motor  to  the 
power  exerted  by  the  tractive  effort, 

2  vVmcaT'          5280       T7/r  , 

-  —  —      —  -  —    —  VT  horsepower. 


33,000         60-33,000 
Solving  this  equation  for  the  car  speed, 

e  Tf 

V  =  0.0714  JL—  Vm  miles  per  hour. 

The  characteristic  curves  of  a  5o-horsepower,  6oo-volt 
General  Electric  Company  direct-current  railway  motor 
(G.E.  No.  2i6A)  are  shown  in  Fig.  23.  They  are  based 
upon  33-inch  car  wheels  and  a  gear  ratio  of  17  to  69,  i.e., 
4.06.  Fig.  24  shows  the  performance  curves  of  the  200- 
horsepower,  55o-volt,  direct-current  motors  used  by  the 
Interborough  Rapid  Transit  Company  of  New  York  City. 
These  curves  are  for  a  gear  ratio  of  20  to  63,  with  33-inch 
car  wheels.  The  characteristic  curves  of  the  25o-horse- 
power,  25-cycle,  225-volt,  gearless  Westinghouse  conduc- 
tively  compensated  single-phase  motors  used  on  the  elec- 
tric locomotives  of  the  New  York,  New  Haven  and  Hartford 


TYPES  AND   PERFORMANCE   CURVES  OF  MOTORS.     49 

Railroad  are  shown  in  Fig.  25.  The  performance  curves  of 
a  2 5o-horsepower,  three-phase,  285o-volt,  2 5-cycle  induction 
motor  for  railway  service  are  given  in  Fig.  26. 

PROBLEMS. 

9.  Plot  a  curve  showing  the  ratio  of  the  current  taken  by  a  compensated 
series  motor  at  synchronous  speed  to  that  taken  at  standstill,  coordinated  to 
the  ratio  of  the  number  of  field  turns  to  the  effective  armature  turns. 

10.  The  motor  of  an  electric  car  having  33-inch  wheels,  when  traveling 
at  25  miles  per  hour,  exerts  a  torque  of  550  pounds  at  one  foot  radius  from 
the  center  of  the 'armature  shaft.     If  the  gear  ratio  be  26  to  60,  and  the  effi- 
ciency of  the  gears  be  97  %,  determine  the  tractive  effort  at  the  base  of  the 
car  wheels,  the  horsepower,  and  the  number  of  revolutions  of  the  motor 
per  minute. 

11.  Determine  the  horsepower  output  and  speed  of  the  induction  motor 
whose  characteristic  curves  are  given  in  Fig.  26,  when  taking  50  amperes 
at  2850  volts.     How  many  stator  poles  has  the  motor? 

12.  The  gearless  25-cycle,  single-phase  motors  used  on  the  New  Haven 
locomotives  have  12  poles.     Determine  the  velocity  of  the  locomotives, 
which  have  drivers  62  inches  in  diameter,  when  the  motors  run  at  synchron- 
ous speed. 

13.  The  total  weight  of  a  Pennsylvania  electric  locomotive  is  166  tons, 
of  which  104  tons  are  carried  by  the  drivers,  and  the  trailing  load  is  550 
tons.     What  is  the  maximum  grade  this  train  can  ascend  with  uniform 
velocity  without  slipping  the  wheels  on  clean  dry  rails?     Neglect  train 
resistance. 


50  TRACTION  AND  TRANSMISSION. 


CHAPTER  IV. 

SPEED   CURVES. 

18.  Motor  Limitations.  —  The  size  of  the  motors  to  be 
installed  on  cars  so  that  they  may  perform  a  proposed 
service  must  be  such  that  the  motors  will  exert  the  necessary 
tractive  effort  for  the  prescribed  acceleration  and  operate 
without  overheating.  As  the  tractive  effort  exerted  by  a 
motor  depends  upon  its  current  intake,  and  the  maximum 
current  which  may  be  supplied  to  the  motor  depends  upon 
commutation,  it  is  seen  that  the  rate  at  which  a  car  may 
be  accelerated  is  dependent  upon  the  allowable  current 
input.  Another  limitation  to  the  rate  of  acceleration, 
besides  the  consideration  of  comfort  to  passengers,  is  ex- 
pressed by  the  coefficient  of  friction  or  adhesion,  that  is, 
the  ratio  of  the  tractive  effort  necessary  to  cause  slipping 
of  the  wheels  on  the  rails  'to  the  total  weight  on  the  drivers. 
This  coefficient  depends  upon  the  condition  of  the  track. 
The  following  values  are  approximate  and  are  based  upon 
a  uniform  torque  exertion: 

Clean  dry  rails o .  30 

Wet  rails 0.18  (with  sand  o . 25) 

Sleet-covered  rails 0.15  (with  sand  0.20) 

Snow-covered  rails '.....  o.  10  (with  sand  o.  15) 

It  is  seldom  necessary  to  apply  motors  to  every  axle, 
economy  dictating  that  the  number  of  axles  equipped  be 
as  small  as  possible  and  as  permitted  by  the  coefficient  of 
adhesion.  In  train  operation  some  cars  are  equipped  with 
motors  while  others  are  mere  trailers  without  motors. 


SPEED   CURVES.  51 

The  heating  of  motors  in  service  is  determined  by  the 
square  root  of  the  mean  square  current  supplied  to  the 
motor  and  the  average  voltage  across  the  motor  terminals. 
This  mean  square  current  is  obtained  from  a  series  of  in- 
stantaneous current  values  taken  over  a  considerable  time 
interval,  as  shown  later.  Thus,  a  motor  should  be  selected 
which  will  commutate  the  abnormal  current  taken  during 
the  period  of  acceleration  without  excessive  sparking  at 
the  brushes  and  also  perform  the  required  service  without 
excessive  temperature  rise. 

19.  Motor  Capacity.  —  To  determine  the  motor  capac- 
ity for  a  proposed  service,  a  knowledge  of  the  load  under 
which  the  motor  must  operate  is  essential.     This  load  is 
of  an  exceedingly  variable  nature,  fluctuating  between  no 
load  at  stopping  points  and  a  maximum  load,  which  occurs 
during  starting  of  the  car.     The  method  of  procedure  is 
as  follows:  a  trial  equipment  is  assumed  (a  guide  to  its 
selection  may  be  obtained  from  a  comparison  of  the  equip- 
ments of  similar  existing  installations),  and  from  the  motor 
performance  curves  there  are  plotted  curves  of  speed  of 
the  car  in  traversing  the  entire  roadway  and  of  motor 
current.     The  former  curve  enables  one  to  foretell  if  the 
prescribed  schedule  speed  can  be  maintained,  allowing  a 
reasonable  margin  for  making  up  delays,  and  the  latter 
curve   serves   as   the  basis   for   determining  whether   the 
assumed  motor  can  perform  the  required  service  without 
such  extreme  heating  as  to  endanger  the  insulation. 

20.  Speed.  —  The  velocity  of  a  car  in  operation  varies 
widely  from  time  to  time.     Starting  from  standstill,  the 
car  is  accelerated,  rapidly  at  first,  then  more  and  more 
slowly  until  a  uniform  speed  is  attained.     After  running 
at  this  speed  for  a  definite  time,  the  current  is  turned  off 


52  TRACTION   AND   TRANSMISSION. 

and  the  car  is  allowed  to  coast,  the  velocity  meanwhile 
gradually  decreasing.  Finally  the  brakes  are  applied  in 
order  to  bring  the  car  rapidly  to  rest  at  the  next  stopping 


Fig.  27- 

point.  Here  freight  or  passengers  are  taken  on  or  dis- 
charged; thereafter  similar  runs  are  performed. 

21.  Typical  Speed  Curves.  —  The  velocity  of  a  car  at 
successive  instants  of  time  may  be  graphically  portrayed 
by  a  speed  curve,  in  which  the  instantaneous  speeds  are 
plotted  in  terms  of  time.  Such  a  curve  takes  the  form 
of  a  series  of  lobes,  each  one  representing  a  run  and  one  of 
which  is  shown  in  Fig.  27.  The  slope  of  the  curve  at  any 
point  indicates  the  time  rate  of  change  of  speed.  This 
slope  may  be  positive,  zero,  or  negative,  corresponding 
respectively  to  acceleration,  uniform  speed,  or  retardation. 

The  speed  curve  may  be  considered  as  made  up  of  four 
parts  as  follows:  starting,  motor,  coasting,  and  braking. 
The  starting  part  corresponds  to  the  period  of  manipula- 
tion of  the  controller,  the  acceleration  of  the  car  and  the 
current  in  the  motor  being  kept  constant,  while  the  voltage 
impressed  upon  the  motor  is  gradually  increased  from  zero 
to  its  normal  value.  The  motor  part  corresponds  to  a 


SPEED   CURVES.  53 

gradual  decrement  of  acceleration  of  the  car  and  of  motor 
current,  normal  voltage  being  impressed  upon  the  motor. 
The  coasting  part  corresponds  to  the  movement  of  the  car 
under  its  own  momentum,  no  current  passing  through  the 
motor.  The  braking  part  corresponds  to  the  period  during 
which  the  car  is  being  quickly  brought  to  rest  by  the 
absorption  of  energy  at  the  brake  shoes.  The  starting 
and  motor  parts  are  often  considered  together  as  constitut- 
ing the  acceleration  part  of  a  speed  curve. 

The  ordinate  B  of  the  speed  curve  represents  the  max- 
imum velocity  of  the  car  during  the  particular  run,  and  the 
horizontal  line  DE  shows  the  duration  of  standstill  at  the 
subsequent  stop.  The  schedule  speed  of  the  car  is  obtained 
by  finding  the  area  of  the  speed  curve  over  the  entire  road- 
way and  dividing  by  the  total  time  taken  therefor  inclusive 
of  stops.  This  time  is  the  interval  between  A  of  the  first 
run  and  E  of  the  last  one.  The  shorter  the  time  of  stops 
the  greater  will  be  the  schedule  speed,  other  conditions 
remaining  unaltered.  The  greater  the  rates  of  acceleration 
and  retardation  the  greater  will  be  the  schedule  speed  pro- 
vided the  same  maximum  speed  is  attained.  If  the  rate 
of  braking  be  too  high  the  car  wheels  will  slide  on  the  rails, 
and  there  will  be  a  tendency  for  the  car  body  to  move  ahead 
over  the  trucks.  The  maximum  practicable  braking  rate 
is  considered  to  be  2.5  jniles  per  hour  per  second. 

22.  Data  for  Plotting  Speed  Curves.  —  The  plotting  of 
a  speed  curve  for  a  proposed  equipment  over  a  typical  run 
requires  a  knowledge  of  the  following  conditions: 

Type  of  motor, 

Number  of  motors  per  car  or  train, 

Motor  performance  curves  at  full  line  voltage  and  at 
a  definite  gear  ratio, 


54  TRACTION   AND   TRANSMISSION. 

Total  weight  of  the  car  with  live  load, 
Plan  and  profile  of  the  roadbed, 
Schedule  speed  required, 
Rates  of  acceleration  and  braking,  and 
Duration  of  stops. 

For  single-car  operation  (double-truck  cars)  a  four- 
motor  equipment  is  preferable,  whereas  for  train  operation 
two-motor  equipments  are  generally  used,  and  sometimes 
both  motors  are  placed  on  one  truck. 

The  performance  curves  of  a  railway  motor  show  its 
characteristics  at  normal  voltage  under  any  load.  When 
starting  the  series  motor,  the  voltage  impressed  upon  its 
terminals  is  low  at  first,  and  is  gradually  increased  by  means 
of  a  controller,  which  cuts  out  resistance  or,  with  single- 
phase  motors,  decreases  the  ratio  of  transformation  of  a 
compensator.  With  suitably  designed  controllers  properly 
operated  the  current  supplied  to  the  motors  will  be  roughly 
uniform  until  the  full  line  voltage  is  impressed  upon  the 
terminals  of  each  motor.  The  torque  exerted,  being  pro- 
portional to  the  current  intake,  will  also  be  approximately 
uniform.  After  the  line  voltage  is  applied  to  the  motors, 
their  performances  are  entirely  dependent  upon  their  char- 
acteristics. 

It  is  essential  to  have  a  reliable  estimate  of  the  weight  of 
the  tentative  car  for  a  proposed  service,  this  weight  to 
include  live  load,  electrical  equipment,  and  brake  apparatus. 
Weights  of  car  bodies  and  trucks  are  given  in  Chapter  I. 
The  average  weight  of  passengers  may  be  taken  as  140 
pounds  per  individual.  The  weights  of  some  standard 
500  to  6oo-volt  electrical  equipments, that  is,  railway  motors 
and  the  accessory  controllers  and  resistances,  made  by 


SPEED    CURVES. 


55 


the  General  Electric  and  the  Westinghouse  Manufacturing 
Companies  for  direct-current  railways  are  given  below. 


Trade 

Name. 

H.P. 

Number 
of 
Motors. 

Type  of 
control. 

Weight  of  each 
motor  including 
gears  and  case, 
in  pounds. 

Weight  of 
control 
apparatus 
in  pounds. 

Total 
weight  of 
equipment. 

GE-54-.. 

25 

2 

K-IO 

1830 

940 

4,600 

4 

K-I2 



H75 

8,495 

W-I2-A.  . 

25 

2 

K-io 

22OO 

940 

5.340 

4 

K-I2 



H75 

9.975 

W-69  .... 

30 

2 

K-io 

1950 

940 

4,840 

4 

K-I2 

H75 

8,975 

GE-78.  .  . 

35 

2 

K-io 

2560 

940 

6,060 

K0o 

4 

-2o 

735° 

11  ,59° 

W-92-A.. 

35 

2 

K-io 

2265 

940 

5.470 

4 

K-28 

. 

1350 

10,410 

GE-70.  .  . 

40 

2 

K-io 

2745 

940 

6,430 

4 

K-28 



1350 

12,330 

W-ioi  .  .  . 

40 

2 

K-io 

2645 

940 

6,230 

4 

K-28 



1350 

n,930 

GE-2i6-A 

50 

2 

K-n 

2885 

1015 

6,785 

4 

K-i4 



2250 

13.790 

4 

Mult.  Unit 



2070 

13,610 

W-Q3-A.. 

50 

2 

K-II 

3355 

1015 

7,725 

4 

K-i4 

2250 

15.670 

GE-87... 

60 

2 

MulLUnit 

35io 

1765 

8,785 

4 

2670 

16,710 

W-85  .... 

75 

2 

4500 

1770 

10,770 

4 



3640 

21,640 

GE-66  .  .  . 

125 

2 

4375 

2715 

11,465 

4 



3750 

21,250 

W-I34-.. 

1  60 

2 



I  2  ,  20O 

4 





26,800 

GE-69  .  .  . 

200 

2 

6230 

338o 

15,840 

4 

5770 

30,690 

The  weights  of  single-phase  motors  somewhat  exceed  the 
foregoing  values  for  the  same  capacity,  but  owing  to  their 
limited  adoption  up  to  the  present  time,  the  design  of  this 
type  of  motor  has  not  yet  become  standardized. 

The  dimensions  of  the  car  chosen  for  the  proposed  rail- 
way should  be  known,  particularly  those  dimensions  which 
limit  the  minimum  permissible  radius  of  track  curvature, 


TRACTION  AND   TRANSMISSION. 


the  clearances  on  each  side  of  the  track  at  curves,  and  the 
maximum  possible  size  of  motor  which  can  be  installed  on 
the  truck. 

The  physical  characteristics  of  a  roadway  are  usually 
embodied  in  a  map  and  profile  of  the  route  showing  the 
length  of  line,  proposed  regular  stations,  junctions  and 
crossings  with  existing  roads,  switches  and  branch  lines, 
and  the  location  and  extent  of  grades  and  curves. 

A  subdivision  of  the  total  length  of  the  road  into  city, 
suburban,  and  interurban  sections  can  usually  be  effected. 
Different  operating  conditions  obtain  in  these  sections, 
because  the  schedule  speeds  and  length  and  frequency  of 
stops  are  not  the  same  for  all.  Representative  values  for 
these  factors  follow. 


Service. 

Schedule  speeds 
in  miles  per 
hour. 

Average  dura- 
tion of  stops 
in  seconds. 

Number  of 
stops  per  mile. 

Interurban  express  
Interurban  local 

35  to  60 
25  to  40 

60 
30 

O.O5  tO  O.  2 

0.3    to  o.  7 

City  rapid-transit  express  .  .  . 
Suburban 

20  to  30 
15  to  20 

25 
15 

0.4    to  i.o 
i    to  2.5 

City  elevated  or  subway 
(local)  

15  tO  20 

12 

2    to  3 

City  surface  lines 

8  to  12 

7 

5    to  10 

The  choice  of  gear  ratio  for  the  trial  equipment  should 
be  such  that  the  peripheral  velocity  of  the  motor  armature 
when  the  car  is  running  at  its  highest  speed  will  not  be 
excessive.  The  ratio  of  the  maximum  speed  to  the  schedule 
speed  varies  between  1.2  and  1.8,  this  ratio  increasing  as 
the  runs  become  shorter  and  the  duration  of  stops  becomes 
longer.  This  enables  the  selection  of  the  proper  gear  ratio. 

23.  Plotting  Speed  Curves.  —  To  understand  the  method 
commonly  used  in  plotting  speed  curves  consider  the  dif- 


SPEED   CURVES.  57 

ferent  portions  of  the  curve  in  Fig.  28  and  the  following 
formula  developed  in  §  1 1 : 

A=^^.  (i) 

ioo  W 

Then  Tm  =  Tt  +  ioo  WA.  (2) 

The  starting  part  of  a  speed  curve  is  taken  as  a  straight 
line,  and  it  passes  through  O,  the  origin  of  time,  at  an 
angle  6 A  with  .the  horizontal  such  that  BA.  =  tan~M,  where 


Fig.  28. 

A  is  the  assumed  constant  rate  of  acceleration  at  starting. . 
It  terminates  at  the  point  A  having  a  speed  ordinate  taken 
from  the  motor  characteristic  curves  for  full  voltage  cor- 
responding to  the  tractive  effort  Tm  calculated  from  equa- 
tion (2),  in  which  Tt  is  based  on  half  schedule  speed. 

The  motor  part  of  the  speed  curve  is  considered  as  made 
up  of  a  series  of  elements  which  are  themselves  straight. 
The  speed  ordinate  of  the  upper  end  of  any  element  is 
assumed,  while  that  of  its  lower  end  is  the  same  as  for  the 
upper  end  of  the  preceding*element.  This  element  makes 
with  the  horizontal  an  angle  0n  =  tan~Mn,  where  An 


58  TRACTION  AND   TRANSMISSION. 

is  the  average  of  the  accelerations  corresponding  to  the 
speeds  at  the  terminals  of  the  element  and  each  calculated 
by  means  of  formula  (i).  The  calculation  of  these  ele- 
ments is  greatly  facilitated  by  two  auxiliary  curves,  one 
showing  the  relation  between  motor  tractive  effort  and  speed 
and  the  other  between  train  resistance  and  speed. 

The  coasting  part  is  generally  assumed  to  be  straight, 
although  it  really  is  concave  towards  the  time  axis.  It  is 
drawn  from  an  assumed  point  B  and  makes  with  the  hori- 
zontal an  angle  QC  =  tan"1  AC,  where  AC  is  calculated 
from  formula  (i),  whose  terms  are  based  upon  the  speed  V 
which  is  the  ordinate  of  the  point  B.  The  other  end,  C,  of 
this  part  of  the  curve  is  determined  by  the  intersection  with 
the  remaining  part. 

The  braking  part  of  the  speed  curve  is  also  assumed  to 
be  straight,  passes  through  the  time  axis  at  D  corresponding 
to  the  specified  expiration  of  the  run,  and  makes  with  the 
horizontal  an  angle  BB  =  tan"  1AB,  where  AB  is  the  assumed 
rate  of  braking.  Its  upper  terminus  is  determined  by  the 
point  of  intersection,  C,  with  the  coasting  part. 

In  plotting  the  different  parts  of  the  curve  on  coordinate 
paper  it  is  inconvenient  to  lay  off  the  angle  B  by  means  of 
a  protractor.  Since 


therefore  At  =  AV/A. 

The  abscissa  increment,  in  seconds,  for  an  element  may  be 
determined  by  dividing  the  speed  increment  in  miles  per 
hour  by  the  average  acceleration  in  miles  per  hour  per 
second.  In  making  calculations  both  Tt  and  W  should  be 
based  upon  the  total  weight  of  car  or  train  divided  by  the 
number  of  motors. 


SPEED   CURVES. 


59 


24.  Numerical  Example.  —  The  process  of  plotting  a 
speed  curve  is  best  illustrated  by  considering  a  specific 
case,  as  follows: 

(a)  Data.  Car,  single  car  to  seat  40  passengers  and  to 
accommodate  an  equal  number  standing,  weighing  with 
trucks  23,650  pounds.  Cross  section,  S  —  95  square  feet. 
Fig.  29  shows  the  relations  which  exist  between  train 


0) 

o 


s 


POU 

»0 

o 


RESISTANCE 

00 

o 


10 


20  30 

SPEED  IN  MILES  PER  HOUR. 

Fig.  29. 


40 


resistance  per  motor,  Tt,  and  speed  calculated  from  the 
formula  given  in  §  n. 

Trial  equipment:  four  direct-current  5o-horsepower, 
600- volt  G.E.  2i6A  motors  with  Type  K-i4  control. 
Characteristic  curves  of  motors  are  shown  in  Fig.  23  for 
a  gear  ratio  of  17  to  69.  From  these  curves  a  new  curve, 
Fig.  30,  of  tractive  effort  per  motor  and  speed  is  plotted 
for  convenience. 


6o 


TRACTION  AND   TRANSMISSION. 


Run,  0.8  mile  run  on  a  straight  level  track.  Schedule 
speed  =  20  miles  per  hour.  Length  of  stop  =  20  seconds. 
Initial  acceleration  rate  =  1.5  miles  per  hour  per  second. 
Braking  rate  =  2  miles  per  hour  per  second. 


900 

g.800 

z 

2 

z  600 

§500 
u. 

^400 

u 

H300 
H200 
100 

\ 

T| 

V 

\ 

\ 

V 

\ 

\ 

\ 

x 

\ 

~^~~ 

•—  —  . 

—  ^— 

10 


20  30 

SPEED  IN   MILES  PER   HOUR. 

Fig.  30. 


40 


The  total  weight  of  the  car  with  live  load  is 

23>65o  +  13,790  +  (80  X  140)=  48,640  pounds 

=  24.32  tons. 

(ti)  Acceleration  at  Subnormal  Voltages.  To  produce  an 
acceleration  of  1.5  miles  per  hour  per  second  requires  a  net 
tractive  effort  of 

T  =  looWA  =  100  •  24.32  •  1.5  =  3648  pounds. 

To  neutralize  train  resistance  during  the  period  of  initial 
acceleration   additional   tractive   effort  must  be   exerted. 


SPEED    CURVES.  6 1 

The  amount  may  be  taken  equal  to  the  train  resistance  at 
half  schedule  speed.  In  this  problem  the  train  resistance  is 

/T^.  ,   WV  ,  SV2 
R  =  50  V  W  +  - 

25        400 

/—  10X24.32      95X10X10 

=  50  v  24.32  +  -        ^^-  +  **-  -  =  280  pounds. 

25  400 

Therefore  the  total  tractive  effort  divided  by  the  number 
of  motors  gives  the  effort  to  be  exerted  by  each  motor  in 
starting,  as 

3648  +  280 

-  =  982  pounds. 
4 

This  tractive  effort  is  produced  when  each  motor  takes 
64  amperes  at  600  volts,  as  shown  by  the  motor  performance 
curves,  Fig.  23 ;  and  the  corresponding  speed  of  the  car  is 
16.9  miles  per  hour.  Thus,  the  current  consumed  as  the 
car  is  accelerated  uniformly  at  the  prescribed  rate  from 
standstill  to  a  speed  of  16.9  miles  per  hour  is  maintained 
roughly  constant  by  the  controller  at  a  mean  value  of 
64  amperes.  The  time  required  to  attain  this  speed  is 

7  =  — —  =11.3  seconds.  This  represents  the  first  point 
A  1.5 

of  the  speed  curve,  and  is  shown  at  A  in  Fig.  3 1 .  Since  the 
acceleration  during  the  first  11.3  seconds  of  the  run  was 
approximately  uniform,  the  speed  curve  over  this  interval 
may  be  drawn  as  a  straight  line,  as  OA . 

(c)  Acceleration  at  Normal  Voltage.  The  full  line  volt- 
age is  applied  to  each  motor  when  the  speed  of  16.9  miles 
per  hour  is  reached,  and  thereafter  the  acceleration  be- 
comes less  and  less  because  the  current  decreases  as  the 
car  speeds  up  and  this  results  in  a  lower  available  tractive 


62  TRACTION   AND   TRANSMISSION. 

effort.  Increased  train  resistance  at  higher  speeds  is  also 
instrumental  in  lowering  the  acceleration  rate.  To  obtain 
other  points  of  the  speed  curve,  the  car  is  supposed  to  be 
running  at  some  higher  speed,  say  20  miles  per  hour.  At 
this  speed  the  motor  current  will  be  48.2  amperes,  the 
total  tractive  effort  will  be  660  pounds  per  motor,  and  the 
train  resistance  will  be  90  pounds  per  motor.  The  net 
tractive  effort  producing  acceleration  is  660  —  90  =  570 
pounds;  whence  the  rate  of  acceleration  at  a  speed  of  20 
miles  per  hour  is 

Ab  =  — — ^7  =  57o-H  iooX  24'3    )  =  0.94  mile  per  hr.  per  sec. 
,  100  W  \  4    / 

The  average  acceleration  during  the  period  in  which  the 
velocity  of  the  car  increased  from  16.9  to  20  miles  per 
hour  may  be  taken  without  serious  error  as  the  mean  of 
the  initial  and  final  acceleration  rates  of  the  period.  The 
time  required  to  gain  this  velocity  increment  is,  of  course, 
the  increment  divided  by  the  average  acceleration,  which 
in  this  case  is 


2O    —    10. 0  •)..!. 

A£  = 2  —  A —  =  2.54  seconds. 

1.5  +  0.94      1.22 

2 

Thus,  the  second  point  of  the  speed  curve  shows  a  veloc- 
ity of  20  miles  per  hour  at  11.3  +  2.54,  or  13.84  seconds 
(b,  Fig.  31). 

This  process  is  continued  with  small  velocity  increments 
until  the  speed  of  the  car  becomes  constant.  A  tabula- 
tion of  the  values  so  obtained  follows;  the  various  points  are 
indicated  on  the  curve.  The  values  of  Tt  in  the  fourth 
column  represent  the  total  train  resistance  divided  by  the 
number  of  motors. 


SPEED   CURVES. 


?' 

1 

1 

1 

1 

1 

1 

1 

UJ 

1 

1 

1 

1 

1 

1 
1 

Q 

_^, 

-^-* 

B.^^' 

1 

.—  •  -* 

^-^ 

-*^i- 

j 

( 

Jr 

^-« 

^ 

-- 

~*  " 

1 

•»- 

— 

1 

^ 

1 

1 

/ 

I 

1 

1 

I 

1 

1 

\ 

I 

1 

1 

1 

\ 

1 

\ 

1 

I 

^ 

\ 

\ 

d 

^ 

\ 

5 

\ 

J 

1 

V 

3 

N 

^^ 

*x 

<; 

>* 

•>^ 

^*-^. 

^ 

^^^ 

*~" 

~*v 

"""N^ 

o                  o                  o                  o 

\J-                            CO                            CM                             *- 

anon  U3d  S3iw 


64 


TRACTION  AND  TRANSMISSION. 


Point. 

Speed, 

Tractive 
effort, 
Tm. 

Train 
resistance, 
Tt. 

Net  trac- 
tive effort, 
Tm~Tt. 

Accelera- 
tion rate, 
A. 

Total 
time. 

A 

16.9 

912 

I  .  "CO 

II    30 

b 

2O 

660 

go 

570 

o 
0.94 

*  *  •  o 
13-84 

c 

22 

530 

96 

434 

0.714 

16.26 

d 

24 

430 

IO2 

328 

0.540 

19-45 

e 

26 

360 

1  08 

252 

0-4I5 

23-65 

f 

28 

300 

H5 

185 

0.304 

29.  22 

I 

30 

255 

122 

133 

o.  219 

36.88 

h 

32 

2  2O 

130 

90 

0.148 

47-78 

i 

35 

170 

145 

25 

0.041 

79.6 

j 

36.8 

152 

152 

o 

0 

177.0 

(d)  Braking.  After  plotting  the  entire  acceleration  curve 
of  a  car  with  an  assumed  electrical  equipment  for  a  partic- 
ular run,  the  speed  curve  is  completed  by  drawing  the 
coasting  and  braking  curves.  Since  the  time  of  passage 
over  a  section  of  the  road  is  specified  by  the  schedule 
speed  and  the  average  duration  of  a  stop,  it  is  necessary 
to  construct  the  braking  curve  first  so  as  to  determine  how 
much  coasting  may  be  permitted  and  still  bring  the  car 
to  the  next  station  in  the  required  time. 

In  the  numerical  illustration  the  car  is  to  travel  0.8  mile 
at  a  schedule  speed  of  20  miles  per  hour,  which  means  that 

the  time  required  for  this  run  is  — =144  seconds. 

20 

But  this  time  includes  a  stop  of  20  seconds;  therefore  the 
actual  running  time  is  124  seconds.  The  braking  curve 
may  now  be  drawn  through  this  point  on  the  time  axis 
at  a  slope  corresponding  to  the  braking  rate  and  extending 
to  its  intersection  with  the  acceleration  curve  at  F.  It 
should  be  drawn  as  a  straight  line,  and,  since  the  braking 
rate  is  specified  at  2  miles  per  hour  per  second,  the  line 
will  pass  through  the  point  which  indicates  that  the  veloc- 


SPEED    CURVES.  .  65 

ity  of  the  car  is  2  X  10  =  20  miles  per  hour  at  a  time  of 
124  —  10  =  114  seconds  from  the  beginning  of  the  run. 

(e)  Coasting.  Since  the  ordinates  of  a  speed  curve  are 
velocities  and  the  abscissae  are  times,  the  area  of  such  a 
curve  will  be  expressed  in  units  of  velocity  X  time,  or 

X  time,  or  simply  in  units  of  distance.     Thus, 

time 

in  Fig.  31,  the  area  of  a  large  square  is  10  miles  per  hour 
X  20  seconds  =  200  mile-seconds  per  hour  =  ?£$s  or  fa 
mile.  The  area  enclosed  by  a  speed  curve  is  therefore  a 
measure  of  the  distance  traversed  by  the  car. 

The  speed  curve  drawn  thus  far  allows  for  no  coasting, 
and  the  area  enclosed  thereby  may  be  less  than,  but  in 
general  wiH  exceed,  that  representing  a  run  of  0.8  mile. 
For  a  run  of  this  length  the  speed  curve  must  enclose 
exactly  0.8  -r-  yV  =  14.4  large  squares.  In  order  to  obtain 
just  this  area,  the  position  of  the  coasting  curve  BC  is 
varied  until  properly  located;  its  slope,  however,  cannot 
be  taken  at  random. 

When  the  current  supply  to  the  motors  is  discontinued 
the  car  tends  to  run  at  constant  speed,  but  train  resistance 
retards  the  motion  and  produces  a  negative  acceleration. 
As  train  resistance  depends  upon  the  speed,  the  coasting 
curve  will  not  be  strictly  a  straight  line,  but  will  have  a 
slight  curvature  tending  to  become  more  nearly  horizontal 
at  lower  speeds.  It  is  usual  to  draw  the  coasting  line 
straight  and  at  a  slope  corresponding  to  the  train  resistance 
value  at  the  speed  at  which  the  car  is  running  when  the 
power  is  cut  off. 

The  coasting  curve  is  drawn  at  the  proper  inclination 
in  a  trial  position  and  the  resulting  area  of  the  speed  curve 
is  determined.  If  the  area  be  different  from  the  proper 


66  TRACTION  AND   TRANSMISSION. 

value  the  line  is  shifted  parallel  to  itself  up  or  down  as  the 
case  may  be,  until  the  enclosed  area  is  found  to  be  correct. 
Should  the  coasting  curve  require  considerable  shifting  so 
that  it  commences  at  a  somewhat  different  speed  value, 
then  its  inclination  must  be  redetermined  on  this  basis. 
The  area  of  the  curve  AFD  of  Fig.  31  is  16.8  large  squares, 
and  the  position  of  the  coasting  curve  was  adjusted  so 
that  the  enclosed  area  A  BCD  is  equal  to  14.4  squares; 
thus  the  speed  curve  truly  depicts  a  0.8  mile  run.  The 
train  resistance  at  the  speed  where  coasting  begins  is  130 
pounds  per  motor.  The  negative  acceleration  produced 

thereby  is    —7-^ — =  0.21   mile  per   hour   per 

100  X  (24.32  -T-  4) 

second,  a  value  giving  the  proper  slope  of  the  coasting  line. 

Had  the  area  of  AFD  been  less  than  14.4  squares,  the 
curve  would  have  indicated  that  the  chosen  equipment  is 
incapable  of  maintaining  the  specified  schedule  speed  under 
the  given  conditions.  In  such  cases  other  curves  should 
be  drawn  for  the  same  equipment  with  lower  gear  ratios, 
or  for  other  equipments  comprising  larger  motors.  On 
the  other  hand,  if  the  excess  area  be  unduly  large,  other 
speed  curves  corresponding  to  higher  gear  ratios  or  smaller 
motors  should  be  constructed.  A  reasonable  margin 
should,  however,  be  allowed  for  making  up  for  delays. 
The  equipment  ultimately  selected  for  the  given  service 
should  be  able  under  emergency  conditions  to  make  a 
complete  trip  in  5  to  15  %  less  running  time  than  that 
allowed  for  regular  service. 

25.  Distance  Curves.  —  Speed  curves  of  cars  over  runs 
having  grades  or  curves  are  more  difficult  to  construct 
than  those  over  a  tangent  level  roadway.  Here  the  addi- 
tional tractive  effort  required  for  propelling  a  car  or  train 


SPEED   CURVES.  67 

up  a  grade  or  around  a  curve  must  be  considered,  and 
indeed,  these  additional  forces  are  applied  at  definite 
places  on  the  run.  This  implies  a  knowledge  of  the  exact 
location  of  the  car  at  every  instant  of  time,  so  that  these 
influences  may  be  properly  represented  on  the  speed  curve. 
The  instantaneous  positions  of  a  car  are  shown  most  con- 
veniently by  a  distance  curve  plotted  in  terms  of  time. 

The  distance  curve  for  the  run  mentioned  in  the  fore- 
going is  plotted  as  follows:  The  average  velocity  over  the 
first  11.3  seconds  of  the  run  is  i  (o  -f-  16.9)  =  8.45  miles 
per  »hour,  and  therefore  the  space  traversed  during  this 

, .    11.3  X  8.45      .,  05.4  X  5280 

period  is  — ^-      -^  mile,  or  ^^  -  =  95.4  X  1.467 

3600  3600 

=  140  feet.  The  average  velocity  over  the  next  2.54  seconds 
is  J  (16.9  +  20.0)  =  18.45  miles  per  hour,  and  the  dis- 
tance traveled  during  this  time  interval  is  18.45  X  2.54  X 
1.467  =  68.6  feet.  This  process  is  continued  over  the 
entire  running  time,  and  the  final  sum  should  be  equal  to 
0.8  X  5280  =  4224  feet.  The  speed  and  distance  curves 
are  generally  plotted  si- 
multaneously, using  for 
convenience  the  same  time 
increment  values. 

26.   Speed  Curve  Plot- 
ting  with    Grades    and 
Curves.  —  As  an  illustra- 
tion   of    the    method   of  Fig  ^ 
plotting  speed  curves  over 

runs  having  grades  and  curves,  consider  the  same  car  and 
equipment  making  a  0.9  mile  run  over  a  roadway  the  plan 
of  which  is  shown  in  Fig.  32 ;  all  other  conditions  to  remain 
unaltered. 


68  TRACTION  AND   TRANSMISSION. 

As  before,  to  produce  an  acceleration  of  1.5  miles  per 
hour  per  second  on  a  level  track  requires 

1.5  X  ioo  X  24'32  =912  pounds  per  motor, 
4 

and  to  overcome  train  resistance  70  pounds  additional 
must  be  exerted.  But  as  the  car  must  be  accelerated  on  a 
2.3  %  up  grade,  a  further  tractive  effort  must  be  exerted 
amounting  to 

20  X  2.3  X  6.08  =  280  pounds  per  motor. 

This  total  force  of  1262  pounds  is  produced  when  -each 
motor  takes  77  amperes,  as  obtained  from  Fig.  23,  and  this 
current  value  is  maintained  moderately  uniform  until  the 
motors  operate  on  the  full  line  voltage  of  600  volts,  which 
occurs  when  the  car  has  attained  a  speed  of  15.3  miles  per 


hour.     The  time  required  therefor  is  =  10.2  seconds, 

and  the  distance  traversed  during  this  interval  with  uni- 


formly accelerated  motion  is  -       X  10.2  X  1.467  =  114  feet. 

These  values  constitute  the  first  points  respectively  of  the 
speed  and  distance  curves  for  this  particular  run,  and  are 
shown  at  A  and  a'  on  the  curves  of  Fig.  33. 

When  the  speed  of  the  car  has  reached  18  miles  per  hour 
the  total  tractive  effort  exerted  by  each  motor  is  840  pounds. 
The  grade  resistance  is  still  280  pounds,  but  the  train 
resistance  at  this  speed  is  now  84  pounds  per  motor.  There- 
fore the  net  tractive  effort  producing  acceleration  is  840  — 
(280  +  84)  =476  pounds;  whence  the  rate  of  acceleration 
at  the  instant  the  velocity  of  the  car  is  18  miles  per  hour  is 

-^—    -  =  0.78  mile  per  hour  per  second. 
ioo  X  6.08 


SPEED   CURVES. 


69 


133J 


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TRACTION  AND   TRANSMISSION. 


The  time  required  for  the  car  to  gain  this  velocity  incre- 
ment of  2.7  miles  per  hour  is 

2.7  -*•  i  (1.5  +  0.78)  =  2.36  seconds, 

and  the  space  traversed  during  this  interval  is 

2.36  X  i  (15.3  +  18.0)  X  1.467  =  57-5 


Thus,  12.56  seconds  after  the  car  started  from  rest  it 
acquired  a  speed  of  18  miles  per  hour  and  covered  a  dis- 
tance of  171.5  feet.  These  values  constitute  second  points 
respectively  on  the  speed  and  distance  curves,  and  are 
indicated  at  b  and  br  in  Fig.  33.  Other  points  are  similarly 
determined,  as  noted  in  the  following  table,  the  process 
being  continued  until  a  distance  of  800  feet  has  been  passed 
over  by  the  car.  At  this  place  the  grade  ceases  and  the 
remainder  of  the  run  is  on  a  level  track. 


a) 

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fl) 

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cd  ^ 

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Time  inc 
ment. 

'£ 

g 

1 

i1 

-0  aJ 

li 

A 

1262 

1  5° 

IO    2 

IO    2 

114  o 

114   O 

b 

18 

840 

84 

476 

0.78 

2.36 

12.56 

57-5 

171-5 

c 

20 

660 

90 

290 

0.48 

3-18 

15-74 

88.6 

260.1 

d 

22 

530 

Q6 

154 

0.25 

5-48 

21  .  22 

168.9 

429 

e 

24 

430 

IO2 

48 

0.079 

12.15 

33-37 

409 

838 

61 

435 

IO2 

53 

0.088 

II  .  21 

32.43 

376 

805 

It  is  seen  in  the  table  that  point  e  was  corrected  in  order  to 
approximate  the  distance  of  800  feet  more  closely. 

Beyond  the  grade  the  net  tractive  effort  for  producing 
acceleration  becomes  larger  by  the  amount  of  280  pounds 
per  motor,  and  thus  the  speed  of  the  car  increases  more 
rapidly  than  before.  Continuing  the  tabulation  until  the 


SPEED   CURVES. 


car  strikes  the  curve,  there  obtains  (compare  with  points 
e  to  h  of  table  of  §  24)  the  following: 


i! 

i 

II 

'rain 
stance. 

tractive 
Tort. 

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26 

360 

1  08 

252 

0.415- 

8-35 

40.78 

305 

IIIO 

f 

28 

300 

115 

185 

0.304 

5-57 

46.35 

220 

I33° 

h 

30 

255 

122 

133 

o.  219 

7.65 

54-0 

326 

1656 

^ 

32 

22O 

130 

90 

0.148 

10.90 

64.9 

495 

2151 

J 

34 

185 

139 

46 

0.072 

18.20 

83-1 

880 

3031 

Ji 

33-3 

I98 

135 

63 

0.104 

10.30 

75-2 

493 

2644 

Since  the  car  encounters  a  curve  after  running  2650  feet, 
a  readjustment  of  point  j  of  the  speed  curve  was  neces- 
sary, because  after  passing  this  place  the  rate  of  accele- 
ration of  the  car  decreases  since  some  tractive  effort  is 
required  to  neutralize  the  increased  flange  friction.  This 
amount  is  Wo°  X  6.08  X  0.5,  or  36  pounds.  The  length  of 


the  curve  is 


=754  feet;  that  is,  the  curve  ends  at  a 


distance  of  3404  feet  from  the  starting  point.  The  figures 
in  the  following  table  refer  to  the  car  movement  on  the 
curve  of  480  feet  radius. 


ii 

1 

II 

~-  <u 

1  1 

ii 

"o'^ 

O  ^ 

"^   § 

a 
1 

•2  ta 

—<     Q 

<S1 

s 

II 

PH  -S2 

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1 

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0. 

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K 

H 

H 

CO 

H 

>fe 

34 

I85 

139 

10 

0.0165 

II  .62 

86.82 

573 

3217 

/ 

34-2 

181 

145 

o 

0 

24.22 

I  I  I  .  04 

1212 

4429 

Had  the  curve  extended  over  a  greater  distance  the  ulti- 
mate velocity  of  the  car  thereon  would  have  been  34.2  miles 


72  TRACTION  AND   TRANSMISSION. 

per  hour;  but  the  curve  ends  before  this  velocity  is  acquired 
and  thereafter  the  car  runs  on  a  tangent  level  track.  The 
time  when  the  car  emerges  from  the  curve  is  shown  by  the 
distance  curve  of  Fig.  33,  and  the  acceleration  curve  from 
this  time  on  may  now  be  completed  along  the  lines  previ- 
ously outlined.  The  braking  and  coasting  curves  are  then 
drawn  in  their  proper  positions,  so  that  the  enclosed  area 
truly  represents  a  0.9  mile  run.  The  completed  speed 
curve  is  shown  as  OABCDE  in  Fig.  33. 

By  reference  to  this  curve  it  is  seen  that  the  power  is 
cut  off  from,  the  car  when  its  velocity  is  32.1  miles  per 
hour  and  when  it  has  been  running  for  65.6  seconds.  Dur- 
ing this  time  the  car  traveled  2175  feet,  as  indicated  by 
the  distance  curve.  While  the  car  is  coasting  for  67.4 
seconds  it  passes  over 

674  X  \  (32.1  +  17.9)  X  1.467  =  2465  feet. 

Thus  the  brakes  are  applied  when  the  car  is  distant  4640  feet 
from  the  starting  point.  The  time  required  to  bring  the 
car  to  rest  from  a  velocity  of  17.9  miles  per  hour  at  the 
prescribed  rate  of  braking  is  8.95  seconds,  and  the  distance 

traveled  during  this  period  is  8.95  X  "•"-  X  1.467  =  117  ft. 

2 

Thus  the  total  length  of  the  run  as  determined  by  summa- 
tion of  the  separate  distances  is  4757  feet,  a  value  which 
exceeds  the  true  length  of  run  by  but  5  feet.  Distance 
curves  therefore  serve  as  admirable  checks  in  the  plotting 
of  speed  curves. 


SPEED   CURVES.  73 


PROBLEMS. 

14.  Plot  a  complete  acceleration  curve  of  a  car  weighing  20  tons  with  live 
load  and  equipped  with  two  5o-horsepower,  direct-current  motors  whose 
characteristic  curves  are  given  in  Fig.  23.     The  initial  acceleration  rate  is 
to  be  1.3  miles  per  hour  per  second  and  the  schedule  speed  is  specified  at 
15  miles  per  hour  on  a  tangent  level  track.     What  is  the  maximum  possi- 
ble velocity  of  this  car  on  such  a  roadway? 

15.  Complete  the  speed  curve  of  the  equipment  mentioned  in  problem  14 
over  a  f-mile  level  roadway,  allowing  a  i5-second  stop  at  the  following  sta- 
tion.    The  braking  rate  is  specified  at  1.5  miles  per  hour  per  second. 

1 6.  What  is  the  shortest  running  time  that  a  motor  car  weighing  43  tons 
total  with  passengers  and  equipped  with   two  2oo-horsepower,  55o-volt, 
direct-current  motors  whose  characteristic  curves  are  shown  in  Fig.  24,  can 
complete  a  one-mile  run  up  a  uniform  grade  of  1.5  %?     The  acceleration 
and  braking  rates  are  2  miles  per  hour  per  second. 

17.  An  8-car   New  York  Subway  train   having  five  motor  cars  each 
equipped  with  two  2oo-horsepower,  500- volt  motors,  weighs  320  tons  in- 
cluding live  load.     The  characteristic  curves  of  the  motors  are  shown  in 
Fig.  24.     Plot  the  acceleration  portion  of  the  speed  curve  for  an  initial 
acceleration  of  two  miles  per  hour  per  second  on  a  tangent  level  track. 

18.  If  the  schedule  speed  of  the  train  in  the  foregoing  problem  is  25  miles 
per  hour  and  the  rate  of  braking  is  2\  miles  per  hour  per  second,  com- 
plete the  speed  time  curve  of  problem  17  for  a  run  of  ij  miles,  allowing  a 
ten-second  stop. 


74  TRACTION   AND   TRANSMISSION. 


CHAPTER  V. 

RAILWAY  MOTOR    CONTROL. 

27.  Direct-current  Control.  —  The  motor-control  equip- 
ment of  an  electric  car  or  train  serves  to  regulate  the 
speed  and  direction  of  rotation  of  the  motors  and  to  govern 
their  action  during  periods  of  initial   acceleration.     The 
most  important  function  of  a  railway  motor  controller  is 
to  maintain  a  sufficiently  uniform  change  of  velocity  during 
initial  acceleration,  due  consideration  being  given  to  the 
durability  of  the  apparatus  and  to  the  comfort  of  passengers. 
Thus  the  variations  in  the  starting  current  from  the  aver- 
age value  necessary  to  produce  the  required  tractive  effort 
for  the  specified  rate  of  acceleration  must  be  so  restricted 
that  the  accompanying  fluctuations  in  torque  will  not  be 
injurious  to  the  equipment  or  unpleasant  for  the  passengers, 
and  the  maximum  current  attained  will  not  give  rise  to 
commutation  difficulties. 

With  direct-current  series  motors  two  general  methods 
of  control  are  in  use:  i,  rheostatic  control,  and  2,  series- 
parallel  control. 

28.  Rheostatic    Method.  —  In    the   rheostatic   method, 
for  use  with  one  or  more  motors,  resistance  is  connected 
in  series  with    the  motor  circuits,  which  is  varied  so  as 
to  regulate  the  voltage  impressed  upon   the    motors.     A 
scheme  of  connection  for  a  rheostatic  railway  controller 
is  indicated  in  Fig.  34.     Successive  portions  of  this  resist- 
ance are  short-circuited  by  closing  switches  i,  2,  3,  and  4. 


RAILWAY  MOTOR   CONTROL.  75 

in  the  order  named,  thus  gradually  increasing  the  pressure 
applied  to  the  motor  terminals.  This  method,  although  sim- 
ple, is  infrequently  employed  because  the  loss  in  the  regulat- 
ing resistance  is  not  conducive  to  economical  operation. 


Fig.  34- 

29.  Series-parallel  Method.  —  The  series-parallel  method 
of  railway  motor  control  is  extensively  used  for  equipments 
with  two  (or  any  multiple  of  two)  motors.  The  car  is 
started  from  rest  and  accelerated  by  first  placing  the  two 
motors  and  a  resistance  in  series  and  then  cutting  out  the 
resistance  step  by  step  until  the  motors  are  operating  in 
series  on  full  voltage.  Since  with  all  the  resistance  cut 
out  there  is  no  unnecessary  PR  loss,  this  is  called  a  running 
connection,  and  the  controlling  mechanism  is  said  to  be 
on  a  running  point.  To  increase  the  speed  further,  the 
motors  are  placed  in  parallel,  with  a  resistance  in  series 
with  both.  This  resistance  is  then  cut  out  step  by  step 
until  the  motors  are  each  operating  on  the  full  line  voltage. 
This  also  constitutes  a  running  connection. 

The  circuits  of  a  series-parallel  controller  are  more  com- 
plex than  those  of  the  rheostatic  type,  since  additional  con- 
nections are  required  to  effect  the  transition  from  the  series 
to  the  parallel  position.  For  accomplishing  this  change 
three  different  methods  may  be  used.  Their  distinctive 
features  are  respectively  (i)  the  shunting  or  short-circuit- 
ing of  one  of  the  motors;  (2)  the  opening  of  the  power 


76  TRACTION  AND  TRANSMISSION. 

circuit;  (3)  the  maintenance  of  full  current  through  all 
motors  during  transition. 

Most  of  the  so-called  Type  K  controllers,  ordinarily 
used  with  single-car  equipments,  operate  according  to  the 
first  method,  the  successive  steps  of  which  are  essentially 
as  follows:  the  starting  resistance  is  gradually  cut  out  until 
the  motors  operate  in  series  on  full  line  voltage ;  thereafter 
a  portion  of  the  total  starting  resistance  is  reinserted  in 
series  with  the  two  motors,  one  of  which  is  then  shunted 
or  short-circuited,  thus  connecting  the  other  motor  across 
full  voltage  but  with  a  protective  resistance  in  circuit. 
The  short-circuited  motor  is  thereafter  connected  in  paral- 
lel with  the  other,  the  resistance  now  being  in  series  with 
both  motors;  this  resistance  is  subsequently  cut  out  in  suc- 
cessive steps. 

The  second  method  of  series-parallel  control,  that  of 
opening  the  power  circuit  during  transition,  exemplified 
by  Type  L  controllers,  is  merely  an  extension  of  the  first, 
intended  for  use  with  motors  of  very  large  capacity.  This 
method  is  now  rarely  employed  because  of  its  inferiority  to 
the  third  method,  which  has  been  developed  to  meet  the 
same  requirements  more  effectively. 

The  third  method  of  transfer  from  the  series  to  the 
parallel  position  is  used  with  multiple-unit  control,  and 
also  applied  to  a  few  Type  K  controllers  designed  to  meet 
the  exacting  conditions  associated  with  large  motor  capacity 
and  high  voltage.  During  transition,  full  current  is  main- 
tained through  all  the  motors  by  means  of  a  "  bridge " 
connection.  A  scheme  of  connections  illustrating  th;s 
type  of  series-parallel  control  is  shown  in  Fig.  35.  The 
controller  performs  the  following  operations:  switches  A 
and  B  are  closed,  thus  placing  both  motors  and  all  the 


RAILWAY   MOTOR    CONTROL.  77 

resistance  in  series  between  the  trolley  or  third  rail  and 
ground.  This  connection,  which  corresponds  to  a  slow  speed 
that  is  suitable  for  switching  in  terminal  yards,  is  passed 
over  quickly  when  accelerating  at  the  usual  rate.  The 
first  movement  of  the  controller  handle  accomplishes  the 
simultaneous  closing  of  switches  5,  6,  and  7.  Switches  i 
to  4  are  then  closed  consecutively,  followed  by  the  closing 
of  switch  C  and  the  subsequent  opening  of  switches  2  to  7 
and  B,  thus -connecting  the  motors  in  series  across  the  line 


2  3  4 

)~| 

6 


c 


M 

LO  O-L-O  0-K>  cJ 
567 

GROUND 

Fig.  35- 

through  the  "bridging"  switch  C.  Thereafter  switches  a 
and  b  are  closed.  Thus  two  currents  will  flow  through 
switch  C  in  opposite  directions,  one  from  the  trolley  through 
the  motors  to  ground  and  the  other  through  the  resistance 
to  ground.  With  properly  proportioned  resistances  prac- 
tically no  current  will  pass  through  C,  and  consequently 
this  "bridging"  switch  may  be  opened,  thereby  placing  the 
motors  in  parallel,  with  resistance  in  series  'with  each. 
After  this,  switches  2  and  5,  3  and  6,  and  4  and  7  are  closed 
progressively,  thus  finally  placing  each  motor  on  full  volt- 
age. This  method  is  desirable  in  that  no  motor  is  sub-, 
jected  to  a  sudden  increase  in  voltage  nor  is  the  circuit 
opened  at  any  time.  Unnecessary  variations  in  torque  are 
therefore  avoided. 


78  TRACTION  AND  TRANSMISSION. 

When  four  motors  are  installed  on  a  car,  they  may  first 
be  connected  in  series,  then  each  pair  in  parallel  with  the  two 
groups  in  series,  and  finally  all  connected  in  parallel ;  this  is 
known  as  the  series,  series-parallel,  parallel  method.  Usually, 
however,  the  motors  are  arranged  in  two  groups,  each  con- 
sisting of  two  motors  permanently  connected  in  parallel  and 
treated  as  a  single  unit  in  so  far  as  their  control  is  concerned. 

30.  Starting  Resistances.  —  The  design  of  starting  re- 
sistances for  use  with  railway  controllers  requires  a  knowl- 
edge of  the  allowable  variation  in  torque  during  accelera- 
tion. When  a  motor  is  started  from  rest  with  resistance 
in  series,  the  current  gradually  decreases  with  increase  in 
speed  because  of  the  generation  of  more  and  more  counter 
E.M.F.,  until  a  portion  of  the  resistance  is  cut  out,  caus- 
ing a  sudden  increase  in  current.  Thereafter  the  current 
gradually  decreases  again  with  further  increase  in  speed 
until  another  portion  of  the  resistance  is  cut  out,  which 
causes  a  sudden  rise  in  current  as  before.  This  current 
fluctuation  continues  until  full  line  voltage  is  applied  to 
the  motor  terminals.  These  current  variations  produce 
corresponding  variations  in  torque,  which,  if  violent,  cause 
unevenness  in  the  velocity  increase  of  the  car,  resulting  in 
discomfort  to  passengers  and  in  severe  mechanical  stresses 
on  the  apparatus.  Experience  shows  that,  in  general,  the 
maximum  and  minimum  values  of  torque  should  not  differ 
from  the  average  value  required  to  produce  the  prescribed 
acceleration  by  more  than  ten  per  cent  of  such  average 
value.  Since  the  iron  of  a  direct-current  series  motor  ap- 
proaches saturation  when  taking  the  large  current  required 
for  starting,  the  torque  exerted  is  approximately  proportional 
to  the  current.  Hence  the  current  is  restricted  to  a  similar 
range  of  variation. 


RAILWAY   MOTOR   CONTROL.  79 

Fluctuations  in  the  current  supplied  to  a  series  motor 
affect  its  field  strength  and  thus  produce  changes  in  the 
counter  electromotive  force  generated,  which  must  be 
considered  in  designing  the  controller  resistances.  The 
necessary  information  relative  to  these  changes  of  counter 
E.M.F.  is  obtained  from  the  saturation  curve  of  the  motor, 
a  curve  which  shows  the  electromotive  force  generated 
in  the  armature  as  a  function  of  the  field  (or  armature) 
current  when-  the  machine  is  driven  at  constant  speed. 
This  curve  is  readily  computed  from  the  resistance  of  the 
motor  and  its  characteristic  curves.  The  electromotive 
forces  corresponding  to  any  given  values  of  current  evi- 
dently bear  the  same  relation  to  each  other  whatever  that 
constant  speed  may  be. 

Rheostatic  Controllers.  The  proper  resistance  units  for 
a  rheostatic  railway  controller  may  be  determined  as 
follows:  ' 

Let  E  =  line  voltage, 

Rm  =  resistance  of  motor, 

r\,  ?2,  Y^  .  .  .  ,  rn  =  the  respective   controller   resistances 

in  series  with  the  motor  when 
the  controller  arm  is  on  contact 
studs  i,  2,  3,  .  .  .  ,  n,  Fig.  36. 

£2,  £3,  .  .  .  ,  En  =  the    respective  counter   electromotive 

forces  generated  at  the  instants 
when  the  arm  makes  contact 
with  studs  2,  3,  4,  .  .  .  ,  n, 

Eit  E2', .  .  .  ,  Enf  =  the  respective    counter   electromotive 

forces  generated  at  the  instants 
when  the  arm  breaks  contact 
with  studs  i,  2,  3,  .  .  .  ,  n, 


8o  TRACTION  AND  TRANSMISSION. 

/  =  average  current  necessary  to  produce  the  required 
tractive  effort  for  the  prescribed  rate  of  accel- 
eration, 

Jmax  =  maximum  current  value  and  7min  =  minimum  cur- 
rent value  as  dictated  by  the  allowable  range 
of  current  variation, 


Fig.   36. 

=  the  electromotive  force  corresponding  to  the  cur- 
rent /max  as  determined  from  the  saturation 
curve,  Fig.  37, 

=  the  electromotive  force  corresponding  to  the  cur- 
rent /min,  Fig.  37, 
and  for  convenience  let 

/^rnax 


and 


K 


At  the  instant  when  the  arm  touches  stud  i,  the  resist- 
ance TI  should  be  such  that  the  current  flowing  through 
the  motor  will  not  exceed  /max;  then 


RAILWAY  MOTOR   CONTROL. 
/  E 

whence  the  total  resistance  of  the  rheostat  is 

E 


81 
(i) 

(2) 


Fig.  37. 

As  the  motor  starts  from  rest  and  accelerates,  the  current 
gradually  decreases,  and  at  the  instant  when  it  reaches  the 
value  7min  the  arm  should  leave  stud  i ;  then 

•n  T-*    / 

(3) 


ri+Rm 

Dividing  (3)  by  (i)  there  results 

£-£/ 


K  = 


E 


which  when  solved  for  E\  gives 


82  TRACTION  AND   TRANSMISSION. 

£l'-£(l-X).  (4) 

At  the  instant  when  the  arm  touches  stud  2  the  motor 
current  should  again  be  /max,  which  is  now  equal  to 

•*max  =          ,     n     '  (5) 


whence 


n  2  (    . 

r2  =  ~ Km- (6) 

J-  rrm.TT  •*•  mftT 


max 


Since  E2  and  £/  are  generated  at  the  same  speed  and 
with  the  respective  field  currents  7max  and  7min,  reference 
to  the  saturation  curve  shows  that 

E2    _  -Emax  _ 
77  /   ~~    T?  ~  Q) 

&\          -timin 

and  therefore 

Ez  =  qEi', 

which,  by  substitution  from  (4),  becomes 

E2=Eq(i-K).  (7) 

At  the  instant  when  the  current  has  again  decreased  to 
7min  the  arm  leaves  stud  2  and 

_E  -  E2'  (, 

Jmin  -IT?'  W 

r2  +  Km 

Dividing  (8)  by  (5), 

7T       E~E* 
K  =  ^^' 

from  which 

EJ  =  E  (i  -  K)  +  KE2, 

whence  by  substitution  from  (7) 

E2'  =  E(i-K)+  EqK  (i  -  K).  (9) 

Proceeding  in  a  similar  manner  there  results 

E         n         E$  ,    N 

r,  = Rm-^-,  (10) 


RAILWAY    MOTOR   CONTROL.  83 

£3  =  g£2'  =  Eq  (i  -  K)  +  E<fK  (i  -  K),  (n) 

Es'=E(i  -K)  +  KE3  =  E(i  -K)+EqK(i  -  K) 

+  EfK*(i-K),  (12) 

and  so  on. 

The  resistance  of  each  of  the  various  steps  may  now  be 
determined;  thus,  subtracting  (6)  from  (2)  and  substitut- 
ing from  (7),  the  portion  between  studs  i  and  2  is 

EZ          E      /         T^x  /     x 

.  ri  -  rz  =  -^  =  —  q  (i  -  K).  (13) 

•*•  max         J-  max 

Similarly, 


-K)=qK(r1-ri),  (14) 

•*  max  •*  max 

r3-n=71-(£4-£3)  =  ;^(i-X)=^(r2-r3),  (15) 

-*  max  1  max 

and  so  on. 

An  expression  for  the  total  number  of  steps  required  may 
be  derived,  but  it  is  more  convenient  to  proceed  by  first 
determining  the  total  resistance  by  equation  (2),  then 
computing  successive  steps  by  equations  (13),  (14),  etc., 
until  the  sum  of  the  resistance  steps  thus  obtained  is  approx- 
imately equal  to  (preferably  equal  to  or  greater  than)  the 
total  resistance.  This  determines  the  number  of  steps  into 
which  the  total  resistance  is  to  be  divided. 

The  foregoing  equations  may  be  used  in  designing  the 
starting  resistances  of  rheostatic  controllers  for  any  num- 
ber of  motors,  connected  in  any  way,  provided  appro- 
priate values  are  substituted  .for  7max  and  Rm.  The  same 
expressions  may  also  be  employed  for  calculating  the  series 
resistance  steps  of  series-parallel  controllers. 

Series-Parallel  Controllers.  The  design  of  the  parallel 
resistance  steps  for  series-parallel  controllers  involves  a  de- 


84  TRACTION  AND   TRANSMISSION. 

termination  of  the  proper  resistances  to  be  connected  in 
series  with  a  motor  (or  motors)  already  in  operation  and 
therefore  generating  a  definite  counter  electromotive  force. 
This  is  a  more  general  problem  of  which  the  preceding  deri- 
vation is  a  particular  case.  Thus,  if  the  controller  shown 
in  Fig.  36  is  to  be  placed  in  series  with  a  motor  that  has 
already  attained  some  definite  speed  because  of  its  previ- 
ous operation  in  series  with  another  motor,  the  equations 
governing  the  design  of  the  rheostat  must  be  modified  as 
follows. 

At  the  instant  when  the  lever  arm  touches  stud  i  the 
current  flowing  is 

T  E  —  EI  ,  ,.\ 

/max  =   -        p  >  (16) 

Ti  +  Km 

where  EI  is  the  counter  electromotive  force  that  is  being 
generated  at  this  instant.  The  other  symbols  retain  their 
former  significance.  Herefrom 


At  the  instant  when  the  arm  leaves  stud  i  the  current 
flowing  should  be  as  before, 


Dividing  (18)  by  (16)  and  solving  for  E\  there  results 

EI  =  E  (i  —  K)  +  KEi.  (19) 

Again,  at  the  instant  when  the  arm  touches  stud  2  the 
current  should  again  be 

/max  =  R*>  (20) 

consequently 


RAILWAY   MOTOR   CONTROL.  85 

E         „          E%  f    x 

r*  =  j  --  Rm~  ~  (21) 

•*•  max  •*•  max 

As  before,  E2  =  qEi, 

whence  by  substitution  from  (19) 

E2  =  Eq(i-K)+  qKEi.  (22) 

The  instant  the  arm  leaves  stud  2  the  current  diminishes  to 

-p  _  -p  / 

/min   =  -       '—£-  (23) 

?2   T  J<m 

Dividing  (23)  by  (20)  and  solving  for  E2', 

E2r  =E(i-K)+  EqK  (i-K)+  qK*Ei.        (24) 
Herefrom 

E        „         EZ  /    \ 

r*  =  j  --  Rm~j^  (25) 

•*-  max  •*  max 

and 


-  K)  +  (fK*Elt    (26) 
and  so  on. 

Proceeding  exactly  as  in  the  foregoing  derivation  there 
are  obtained  the  following  expressions  for  the  resistances 
of  the  various  steps  of  the  controller: 


f2  -ra  =  -p-  (£3  -  E,)  =  qK  (n  -  ra),  (28) 

^max 

^3-^4=  y  —  (£4  -  £3)  =  ^£  (^2  -  fs),  (29) 

-^max 

and  so  on. 

If  the  controller  having  the  resistance  steps  under  con- 
sideration is  to  be  used  in  starting  a  motor  (or  motors) 
from  rest,  EI  is  equal  to  zero  and  the  equations  reduce  to 
the  forms  previously  derived.  If,  however,  the  motor  is 
already  in  operation,  E\  will  have  some  value  greater  than 


86  TRACTION   AND   TRANSMISSION. 

zero.  In  calculating  the  parallel  resistance  steps  of  a 
series-parallel  controller,  this  value  may  be  determined 
from  the  fact  that  the  total  resistance  for  parallel  operation 
should  be  of  such  magnitude  as  to  allow  the  current  to 
increase  from  7mjn  to  7max  when  the  motors  are  transferred 
from  the  series  to  the  parallel  connection.  Herefrom  it 

follows  that  ^          „ 

£1  =  q£8, 

where  Ea  is  the  counter  E.M.F.  per  motor  at  the  instant 
when  the  series  connection  is  interrupted.  Since  the  total 
counter  E.M.F.  generated  when  the  motors  are  running 
in  series  without  resistance  is  equal  to  the  line  voltage 
minus  the  total  resistance  drop,  the  value  of  Es  may  readily 
be  obtained  in  any  given  case.  Thus,  for  a  two-motor 
equipment 

Et-qE.-q®-2^"***-  (30) 

A  definite  knowledge  of  the  resistance  of  the  motor  con- 
nections and  car  wiring  is  conducive  to  even  greater  accu- 


Fig.  38. 


racy  in  the  determination  of  the  controller  resistance  units. 
A    three-point    grid    resistance    manufactured    by    the 
Westinghouse  Electric  Company  is  shown  in  Fig.  38. 


RAILWAY  MOTOR   CONTROL.  87 

31.  Numerical  Example.  —  As  an  illustration  of  the 
method  of  applying  the  foregoing  equations  to  the  calcu- 
lation of  resistance  steps,  consider  the  design  of  a  series- 
parallel  Type  K-io  controller  for  use  on  a  car  equipped 
with  two  35-horsepower,  500- volt  motors.  The  saturation 
curve  of  the  motors  is  shown  in  Fig.  39,  and  the  resistance 


MEGAMAXWELLS 

_  10  05 

O  o  o  o 

^^- 

^ 

""" 

^ 

^> 

/f 

/ 

/ 

7 

/_ 

10         20         30        40         50        60         70        8( 

AMPERES 
Fig.  39. 

of  each  motor  is  1.18  ohms.  The  operating  conditions 
are  such  that  an  average  starting  current  of  60  amperes 
per  motor  is  necessary  to  produce  the  prescribed  initial 
acceleration  rate,  and  the  controller  specifications  require 
that  the  limiting  values  of  current  shall  not  differ  from  this 
average  value  of  60  amperes  by  more  than  10  %. 
In  this  problem 


7max  =.6o  X  i.i  =  66  amperes, 
60  X  0.9  =  54  amperes, 


and  therefore 


88  TRACTION  AND  TRANSMISSION. 


and 

qK  —  i.i  X  0.818  =  0.90. 

The  total  starting  resistance  required  for  the  operation 
of  the  two  motors  in  series  is 


'COO 

ri  =  ^-  —  2  X  1.18  =  7.58  —  2.36  =  5.22  ohms, 
oo 

and  the  various  series  resistance  steps  into  which  it  is 
divided  are: 

500  X  I.I/  0    0\  -U 

r\  —  TI  =  ^—        —  (i  —  0.818)  =  1.52  ohms. 
66 

r%  —  YZ  =  0.9  X  1.52  =  1.37  ohms, 

r*  —  r±  =  0.9  X  1.37  =  1.23  ohms, 
and 

^4  —  f5  =  0.9  X  1.23  =  1.  1  1  ohms, 

making  a  total  of  5.23  ohms. 

The  counter  E.M.F.  generated  at  the  instant  when  the 
motors  are  placed  in  parallel  is 

„       i.i  (500  -  2  X  1.18  X  54) 

—  - 


=  205  volts. 


In  Type  K-io  control  the  two  motors  are  placed  in 
parallel,  with  the  same  resistance  in  series  with  both. 
Hence  the  total  resistance  required  for  parallel  operation  is 

500       1.18       205  f  , 

fl=  -      "  -  -          =3.79-(o.S9+i.SS)  =  i.6S  ohms, 


and   the  various  parallel   resistance   steps  into  which  it 
should  be  divided  are: 


RAILWAY  MOTOR   CONTROL.  89 


=  0.758  —  0.155  =  0.603  ohms, 

r<i  —  rs  =  0.9  X  0.603  =  °-543  ohms, 
and 

7-3  —  r±  =  0.9  X  0.543  =  0.489  ohms, 

constituting  a  total  of  1.635  ohms. 

32.  Alternating-current    Control.  —  Single-phase    series 
motors  in  raihvay  service  are  controlled,  like  direct-current 
motors  of  the  series  type,  by  varying  the  pressure  applied 
to  their  terminals.     This  variation  may  be  effected  by  the 
standard  direct-current  method  previously  described.  More 
efficient  means  of  potential  regulation  are,  however,  avail- 
able with  alternating  current,  so  that  the  large  PR  loss 
incident  to  the  use  of  starting  resistances  may  be  avoided 
and  a  greater  number  of  running  points  obtained.     Two 
general  methods  of  control  peculiar  to  alternating  currents 
are  at  present  employed  with  single-phase  equipments  :  i  ,  the 
induction  regulator,  and  2,  the  compensator  method. 

33.  Induction  Regulators.  —  In  starting  a  car  by  the 
former  method    the  voltage   impressed  upon    the   motor 
terminals  is  gradually  increased  by  means  of  a  single-phase 
induction  regulator.     This  device  is  essentially  a  trans- 
former of  which  one  coil  is  movable  with  respect  to  the 
other,  the  windings  being  arranged  in  a  manner  similar 
to  those  of  a  coil-wound  induction  motor.     The  primary 
coil  is  usually  connected  to  suitable  taps  on  an  autotrans- 
former  or  compensator,  used  to  step  down   the  voltage. 
The  secondary  coil  is  placed  in  series  with  the  motor  cir- 
cuit, which  is  likewise  connected  to  transformer  taps  of 
suitable  potential.     By  changing  the  relative  position  of 
the  regulator  coils  the   effective  E.M.F.  induced  in  the 


QO  TRACTION  AND   TRANSMISSION. 

secondary  winding  of  the  regulator  may  be  varied  from 
zero  to  a  definite  maximum  value  in  either  direction,  that 
is,  in  phase  with  or  in  phase  opposition  to  the  E.M.F. 
impressed  upon  the  motor  circuit  by  means  of  the  trans- 
former. Thus,  if  Et  is  the  E.M.F.  between  the  transformer 


—  GROUND 

Fig.  40. 

taps  to  which  the  motor  circuit  is  connected,  and  Er  is 
the  maximum  E.M.F.  induced  in  the  secondary  coil  of  the 
regulator,  then,  neglecting  the  impedance  drop  in  the 
wiring,  the  pressure  applied  to  the  motors  may  be  varied 
through  all  values  from  Et  —  Er  to  Et  +  Er  according  to 
the  cosine  of  the  angle  of  displacement  between  the  axes 
of  the  two  windings.  This  method  of  control  is  illustrated 
by  the  scheme  of  connections  shown  in  Fig.  40,  where  C 
is  the  autotransformer  which  is  connected  across  the  line, 
S  is  the  secondary  coil  of  the  induction  regulator  and  is  in 


RAILWAY  MOTOR   CONTROL. 


91 


series  with  the  motor  circuit,  and  P  is  the  primary  coil 
thereof,  which  in  this  case  is  the  movable  element  of  the 
regulator.  Evidently  every  possible  position  of  the  control- 
ler will  result  in  a  definite  voltage  upon  the  motors,  so  this 
method  of  control  may  be  considered  as  yielding  a  mul- 
tiplicity of  running  positions.  The  induction  regulator 
method  therefore  possesses  the  important  advantage  of 
giving  an  extremely  uniform  rate  of  acceleration.  The 
large  weight  and  low  power  factor  of  the  regulators,  and  the 
complicated  mechanism  required  for  their  operation,  such 
as  gears  and  levers,  are,  however,  serious  objections  which 
tend  to  retard  the  further  adoption  of  this  type  of  control. 


O — nftflTH 


1  O 


TO  MOTORS 


Fig.  41. 


34.   Compensators.  —  In    the    compensator   method   of 
control  the  voltage  at  the  motors  is  regulated  by  varying 


92 


TRACTION  AND   TRANSMISSION. 


the  ratio  of  transformation  of  a  compensator,  which  serves 
also  as  a  step-down  transformer  in  those  installations  where 
high  trolley  potentials  are  used.  One  terminal  of  the  motor 
circuit  is  connected  to  ground.  The  other  terminal  may  be 
successively  connected  to  a  series  of  compensator  taps  so 
arranged  that  during  initial  acceleration  the  E.M.F.  applied 
to  the  motor  circuit  may  be  increased  in  suitable  steps 
until  each  motor  operates  on  rated  voltage. 

The  connections  of  a  compensator-type  controller  should 
be  such  that  the  transition  from  one  compensator  tap  to 
another  may  be  effected  without  interrupting  the  motor 
current  or  short-circuiting  any  portion  of  the  compensator 
winding.  For  example,  in  transferring  the  motor  connec- 
tion from  tap  i  to  tap  2  of  the  compensator  C,  shown  in 
Fig.  41,  an  uninterrupted  flow  of  current  through  the 
motors  is  maintained  by  closing 
switch  2  before  switch  i  is  opened. 
In  order  that  this  procedure  may 
not  short-circuit  the  portion  of  the 
compensator  winding  included  be- 
tween taps  i  and  2,  a  preventive  coil 
P  is  connected  in  series  with  switch 
2  as  shown.  The  resistance  R  and 
the  reactance  X  of  this  preventive 
coil  are  so  proportioned  that  the  im- 
pedance drop  Z/,  resulting  from  the 
passage  of  the  motor  current  /,  is 
equal  in  magnitude  and  opposite  in 
phase  to  the  voltage  E  existing  be- 
tween taps  i  and  2  of  the  com- 
This  relation  is  indicated  by  the 
vector  diagram  of  Fig.  42,  where  0  is  the  angle  by  which 


Fig.  42. 

pensator    winding. 


RAILWAY   MOTOR   CONTROL.  93 

the  motor  current  lags  behind  the  pressure  E,  which  is  of 
course  in  phase  with  the  voltage  impressed  upon  the  motor 
circuit  by  means  of  the  compensator.  It  is  evident  from 
this  figure  that  the  values  of  resistance  and  reactance 
required  depend  on  the  power  factor,  cos  0,  of  the  motor 
circuit.  Since  the  power  factor  varies  through  a  consider- 
able range  during  the  period  of  uniform  acceleration,  it  is 
desirable  to  connect  in  series  with  each  compensator  switch 
a  preventive -coil  designed  to  meet  the  particular  conditions 
obtaining  at  the  instant  when  that  switch  is  closed.  This 
method  of  control  has,  however,  the  disadvantage  of  requir- 
ing a  relatively  large  number  of  preventive  coils  no  two  of 
which  have  the  same  constants,  yet  each  must  be  designed 
to  carry  the  full  motor  current. 

In  the  so-called  multiple-switch  method  of  compensator 
control,  now  extensively  employed,  the  preventive  coils 
are  used  as  auto-transformers  to  divide  the  motor  current 
between  two  or  more  compensator  switches.  Thus,  at 
each  running  point  of  the  controller  the  motor  circuit  is 
connected  to  a  set  of  two  or  more  successive  compensator 
taps,  each  of  which  supplies  a  definite  fractional  part  of  the 
motor  current.  The  essential  features  of  this  method  are 
illustrated  in  Fig.  43.  In  the  particular  scheme  of  connec- 
tions there  depicted,  three  preventive  coils  are  used  to 
divide  the  motor  current  into  four  approximately  equal 
parts.  The  first  running  position  of  the  controller  is  at- 
tained by  closing  switches  i,  2,  3,  and  4.  The  voltage 
applied  to  the  motor  circuit  when  the  controller  is  in  this 
position  is  evidently  equal  to  the  potential  relative  to 
ground  of  a  point  on  the  compensator  winding  midway 
between  taps  i  and  4.  When  the  controller  handle  is 
moved  to  the  second  running  position  switch  i  is  opened, 


94 


TRACTION  AND  TRANSMISSION. 


followed  by  the  closing  of  switch  5.  Similarly,  to  pass  to 
the  third  running  point,  switch  2  is  opened  and  then  switch 
6  is  closed;  and  so  on  until  the  motors  are  supplied  with 
current  at  rated  voltage  through  switches  5,  6,  7,  and  8. 
It  is  obvious  that  during  transition  from  one  running  point 


TO  MOTORS 


"GROUND 


Fig.  43- 


to  another  the  full  motor  current  is  maintained  without 
short-circuiting  any  portion  of  the  compensator  winding. 
Since  each  switch  is  required  to  handle  only  a  fractional 
part  of  the  total  current  supplied  to  the  motor  circuit,  this 
method  is  well  suited  for  use  with  railway  equipments  of 
large  capacity. 

In  cases  where  single-phase  series  motors  are  required  to 


RAILWAY  MOTOR   CONTROL.  95 

operate  on  direct  current  over  a  portion  of  the  roadway, 
some  form  of  rheostatic  or  series-parallel  control  must  be 
installed  for  use  during  the  periods  of  direct-current  oper- 
ation. The  losses  that  would  result  from  the  use  of  start- 
ing resistances  during  the  intervals  of  alternating-current 
operation  are,  however,  in  general  sufficient  to  justify  the 
installation  of  compensator  control  for  use  on  the  sec- 
tions where  alternating  current  is  employed.  This  com- 
pensator may  constitute  a  part  of  the  autotransformer 
which  is  used  to  step  down  the  high  trolley  voltage  asso- 
ciated with  alternating-current  traction  to  a  lower  value 
which  is  suitable  for  motor  operation.  The  use  of  com- 
pensator control  on  road  sections  supplied  with  alternating 
current  therefore  involves  little  additional  expense. 

35.  Induction  Motor  Control.  —  The  methods  of  control 
required  with  three-phase  induction  motors  are  essentially 
different  from  those  employed  with  alternating-current  rail- 
way motors  of  the  series  type.  The  latter  methods  are  not 
applicable  to  induction  motors  in  railway  service,  since 
the  reduction  in  impressed  voltage  necessary  in  starting 
by  any  of  these  methods  causes  a  prohibitive  decrease  in 
the  capacity  of  such  machines.  The  following  methods  are, 
however,  available  for  the  control  of  three-phase  induction 
motor  equipments:  (a)  variable  resistances  in  the  second- 
ary circuits  of  the  motors;  (b)  changing  the  number  of 
poles  of  the  motors;  (c)  cascade  operation  of  the  motors. 

(a)  Variable  -Resistance  Method.  The  insertion  of  vari- 
able external  resistances  in  series  with  each  phase  of  the 
secondary  windings  of  the  motors  by  means  of  suitable 
slip  rings  constitutes  the  principal  method  of  maintaining 
an  approximately  uniform  torque  during  the  periods  of 
initial  acceleration.  These  resistances  are  so  proportioned 


96  TRACTION  AND   TRANSMISSION. 

that  the  motor  exerts  at  starting  a  torque  sufficient  for  the 
prescribed  acceleration  rate.  As  the  speed  of  the  motor 
increases,  causing  a  decrease  in  the  E.M.F.  induced  in 
the  rotor  windings,  the  external  resistances  are  cut  out 
successively,  thereby  maintaining  a  moderately  constant 
secondary  current  and  thus  uniformly  increasing  the  speed 
at  which  the  motor  exerts  the  definite  torque  required. 
While  this  method  possesses  the  advantage  of  simplicity, 
it  does  not  permit  of  efficient  acceleration  because  of  the 
PR  losses  in  the  rotor  resistances.  It  also  provides  for 
only  one  efficient  running  speed,  since  the  induction  motor 
is  practically  a  constant-speed  machine,  the  slip  rarely 
exceeding  10  %  of  the  synchronous  speed  which  the  motor 
closely  approaches  when  the  car  runs  at  its  ultimate  veloc- 
ity on  a  level  roadway.  It  is  therefore  desirable  to  employ 
in  connection  with  this  resistance  method  of  control  some 
means  of  changing  the  synchronous  speed  of  the  motors, 
thereby  reducing  the  PR  losses  during  acceleration  and 
providing  for  one  or  more  additional  running  speeds. 

(b)  Variable  Multipolarity  Method.  In  the  second  method 
of  control  the  synchronous  speed  of  the  motors  is  varied  by 
changing  the  number  of  motor  field  poles.  If  the  frequency 
of  the  voltage  be/  cycles  per  second,  the  synchronous  speed 
in  revolutions  per  minute  is 


m 

P 

where  p  is  the  number  of  pairs  of  poles  on  the  induction 
motor. 

In  order  to  change  the  number  of  poles  of  a  given  induc- 
tion motor  it  is  necessary  either  to  provide  two  or  more 
separate  windings,  each  of  which  is  designed  to  yield  a 


RAILWAY  MOTOR   CONTROL. 


97 


different  number  of  poles,  or  to  employ  a  single  winding  so 
arranged  that  the  number  of  poles  which  it  produces  may 
be  altered  by  a  suitable  change  in  the  connections  between 
the  various  parts  of  the  winding  and  the  three-phase  line. 
The  latter  method  is  the  more  desirable  since  no  inductors 
are  idle  during  operation. 

A  simple  arrangement  of  windings  for  carrying  out  this 
method  is  illustrated  in  Fig.  44,  which  shows  the  stator 
winding  of  one  phase  of  an  8-pole  —  4-pole,  three-phase  in- 
duction motor.  The  complete  phase  winding  1-3  is  divided 


IN  O  IN 

A     A 


S         [8  POLES] 
[4  POLES! 


1 

2 

3 

4 

5 

6 

7 

8 

1 

\ 


\ 


\ 


o 

1  3  2 

Fig.  44- 

into  the  two  parts  1-2  and  2-3  by  a  tap  2  at  the  middle 
point  of  the  winding.  Terminals  i  and  3  connect  with  the 
windings  of  the  two  other  phases,  which  for  clearness  are 
not  shown  in  this  figure.  The  winding  shown  in  Fig.  44 
differs  from  the  usual  induction  motor  winding  in  that  only 
alternate  poles  are  wound.  To  produce  an  8-pole  magnetic 
field  the  windings  2-1  and  2-3  are  placed  in  parallel  with  each 
other  by  connecting  tap  2  to  one  of  the  line  wires  and  taps 
i  and  3  to  the  neutral  point  of  the  phase  windings.  The 
coils  are  so  arranged  that  when  thus  connected  they  pro- 


98 


TRACTION  AND   TRANSMISSION. 


duce  poles  which  are  all  of  the  same  polarity.  Interme- 
diate poles  of  opposite  polarity  will  therefore  be  formed 
between  them,  thus  producing  an  8-pole  field  as  indicated. 
If,  however,  a  4-pole  field  is  desired,  windings  1-2  and 
2-3  are  placed  in  series  by  connecting  terminals  i  and  3  to 


line  wires  of  the  three-phase  supply.  One  of  the  windings 
is  thereby  reversed  with  respect  to  the  other  and  conse- 
quently the  poles  pertaining  thereto  will  be  of  opposite 
polarity.  The  intermediate  poles  will  then  disappear,  re- 
sulting in  a  4-pole  field.  Fig.  45  shows  the  schematic  ar- 
rangement and  the  controller  connections  for  simultaneously 
changing  the  number  of  poles  of  all  three  stator  phases. 


RAILWAY   MOTOR   CONTROL.  99 

(c)  Cascade  Method.  The  third  method  of  three-phase 
induction  motor  control  consists  in  operating  two  motors 
in  cascade.  In  the  cascade  connection,  or  concatenation, 
of  two  induction  motors,  the  rotors  of  both  machines  are 
mounted  on  the  same  shaft  or  otherwise  mechanically 
coupled  as  by  gears  or  connecting  rods.  The  primary  of 
the  first  motor  is  connected  to  the  line  and  its  secondary 
is  connected  to  the  primary  of  the  second  motor.  The 
secondary  windings  of  the  latter  machine  are  short-cir- 
cuited through  suitable  starting  resistances. 

When  two  induction  motors  are  started  in  cascade  con- 
nection, the  power  output  of  the  first  machine  consists  in 
part  of  mechanical  power  delivered  to  the  rotor  shaft  and 
in  part  of  electrical  power  supplied  to  the  primary  of  the 
second  machine.  During  initial  acceleration,  the  torque 
exerted  by  such  a  cascade  set  is  maintained  approximately 
constant  by  progressively  cutting  out  the  starting  resist- 
ances. Thereafter  the  torque  decreases  with  further  in- 
crease in  speed,  approaching  zero  as  the  slip  of  the  second 
motor  decreases  toward  zero.  Thus  two  motors  connected 
in  cascade  approach,  when  operating  under  light  loads,  a 
definite  limiting  speed,  which  may  be  determined  as  follows: 
Let  /  =  the  frequency  of  the  line  E.M.F., 

Vi  =  the  synchronous  speed  of  the  first  motor  in  rev. 

per  min., 
Vi=  the  synchronous  speed  of  the  second  motor  in 

rev.  per  min., 

V  =  speed  of  rotor  shaft  in  rev.  per  min., 
pi  =  number  of  pairs  of  poles  of  the  first  motor, 
p2  =  number  of  pairs  of  poles  of  the  second  motor, 
^i  =  slip  of  the  first  motor, 
s2  =  slip  of  the  second  motor. 


and 


100  TRACTION  AND  TRANSMISSION. 

Then 

Fl  ==    Pi 

*lL  =  6o//Fi  -  F\  =  6o//         FA 
>2       =  p2  (     F!     /=:   p*  V1    "FiA 

which  by  substitution  from  equation  (i)  becomes 

F2  =  -^— — —  -  (2) 

Since 

F2-  F 
52  =  — F ' 

therefore 

F=F2(i-.2).  (3) 

Substituting  in  equation  (3)  the  value  of  F2  given  in  equa- 
tion (2),  there  results 


which  shows  that  as  s2  approaches  zero  F  approaches  the 

limiting  speed, 

6o/ 

#!.'+'.#»" 

Hence  the  synchronous  speed  of  the  two  motors  connected 
in  direct  concatenation  is  the  same  as  that  of  a  single 
motor  having  pi  +  pz  pairs  of  poles. 

Two  similar  induction  motors  connected  in  cascade 
share  the  load  with  approximate  equality;  thus  the  second 
motor  utilizes  a  considerable  portion  of  the  energy  that 
would  otherwise  be  consumed  in  the  starting  resistances 
when  operating  at  speeds  below  the  synchronous  speed  of 
the  combination.  At  the  latter  speed,  however,  the  torque 
exerted  is  zero,  and  with  further  increase  in  speed,  such  as 


RAILWAY  MO^Oj     CONTRA. J^    ^.^^  -      IOI 

occasioned  by  running  down  grades,  the  torque  becomes 
negative  and  the  cascade  set  operates  as  a  generator,  return- 
ing energy  to  the  line. 

In  most  cases  of  cascade  control  the  motors  are  divided 
into  groups,  each  of  which  consists  of  a  main  motor  and  an 
auxiliary  motor,  the  latter  being  employed  during  cascade 


Fig.  46. 

operation  only.  In  starting,  each  auxiliary  motor  is  con- 
nected in  cascade  with  the  corresponding  main  motor, 
and  the  starting  resistances  in  the  secondary  circuits  of 
the  former  are  cut  out  in  successive  steps.  The  cascade 
connection  is  then  broken  by  short-circuiting  the  second- 
ary windings  of  the  main  motor  through  the  starting 
resistances,  which  are  thereafter  cut  out  progressively  as 


102 


t    RANSMISSION. 


before.  Thus  the  auxiliary  motors  are  required  to  operate 
only  intermittently  on  a  low  voltage,  and  the  full-speed 
power  factor  of  the  main  motors  is  higher  than  would  be 
the  case  if  their  load  were  shared  with  the  auxiliary  motors 
by  connecting  the  latter  across  the  line.  Fig.  46  shows 
a  scheme  of  connections  for  carrying  out  this  method  of 
control. 

36.  Controllers.  —  All  types  of  railway  motor  control 
must  include  means  for  changing  the  direction  of  rotation 
of  the  motors.  A  series  motor  is  reversed  by  interchang- 
ing the  connections  of  either  its  field  or  its  armature  wind- 
ings. With  a  three-phase  induction  motor  the  same  result 
is  obtained  by  exchanging  the  connections  of  any  two  of  the 
three  leads  that  supply  the  motor  with  current. 

Hand  Control.  —  The  manipulation  of  the  switches  is  ac- 
complished directly  by  hand  or  through  the  intervention 
of  an  auxiliary  control.  In  the  former  system  a  motorman 
makes  the  necessary  electrical  connections  by  moving  a 
handle  at  the  top  of  a  controller  on  the  car  platform.  The 
movement  of  this  handle  causes  the  rotation  of  a  vertical 
cylinder  and  thus  permits  of  the  successive  connection 
of  various  contact  studs  thereon  with  stationary  fingers, 
which,  by  means  of  suitable  car  wiring,  are  properly  con- 
nected to  the  trolley  or  third  rail,  to  the  motors,  and 
to  the  different  rheostat  terminals  or  compensator  taps. 
Fig.  47  shows  a  Westinghouse  controller,  for  series-parallel 
operation,  with  the  cover  removed.  It  has  seven  control- 
ling points  in  the  series  position  and  six  in  the  parallel 
position,  and  the  motors  are  short-circuited  during  the 
transition  period.  The  direction  of  rotation  of  the  motors 
is  changed  by  moving  a  reversing  lever  and  thus  actuating 
a  smaller  cylinder  which  is  mounted  beside  the  main  cylin- 


RAILWAY  MOTOR   CONTROL. 


I03 


der  of  the  controller  and  is  provided  with  suitable  contact 
pieces  for  effecting  the  necessary  change  in  connections.  In- 
terlocking devices  are  supplied,  so  that  the  reversing  handle 
cannot  be  moved  unless  the  controlling  handle  is  in  such 
a  position  that  connection  with  the  trolley  or  third  rail  is 


Fig.  47- 

broken.  The  controlling  handle  also  cannot  be  moved  if 
the  reversing  handle  is  not  properly  set  either  for  forward 
or  backward  motion  of  the  car.  The  reversing  handle  can 
be  removed  from  the  controller  only  when  in  its  neutral 
or  "off"  position,  to  which  it  cannot  be  turned  unless  the 
controlling  handle  is  also  in  its  "  off  "  position,  thus  entirely 
disconnecting  the  motor  circuits  from  the  trolley  or  third 


104  TRACTION  AND  TRANSMISSION. 

rail.  Cut-out  switches  are  provided,  so  that  a  defective 
motor  or  group  of  motors  may  be  disconnected  without 
interfering  with  the  operation  of  the  remaining  motor  or 
motors.  As  serious  arcs  are  liable  to  ensue  upon  breaking 
a  circuit  of  500  volts,  the  contact  pieces  and  fingers  are 
separated  from  adjacent  ones  by  strips  of  insulating  mate- 
rials, which  are  usually  fastened  to  the  inside  of  a  separate 
cover.  Such  arcs  are  effectively  disrupted  by  the  field  of 
an  electromagnet,  which  is  an  essential  part  of  controllers 
used  with  motors  of  large  capacity. 

In  operating  an  electric  car  equipped  with  hand  control 
the  power  should  never  be  turned  off  by  a  slow  reverse 
movement  of  the  controller  handle,  as  destructive  arcs 
are  liable  to  occur  upon  a  slow  break.  To  lower  the  speed 
of  a  car,  the  power  should  be  completely  and  suddenly 
shut  off.  Before  the  car  has  slackened  its  speed  too  much 
the  controller  handle  can  be  brought  up  to  the  proper 
point. 

Multiple-Unit  Control.  —  The  system  of  mo  tor  control  in 
which  the  switches  are  operated  electrically  or  pneumatically 
through  the  intervention  of  an  auxiliary  circuit  is  called  the 
multiple-unit  system,  since  it  is  designed  for  the  operation 
of  several  motor  cars  coupled  together  in  a  train,  all  the 
motors  being  controlled  simultaneously  from  any  master 
controller  on  the  train.  This  system  is  now  extensively 
employed  not  only  for  the  operation  of  trains  made  up  of 
motor  cars  and  trailers  but  also  for  the  control  of  electric 
locomotives  and  single-car  equipments  of  large  capacity. 
The  control  apparatus  for  each  motor  car  or  locomotive 
consists  of  a  motor  controller  and  two  master  controllers. 

The  motor  controller  is  composed  of  a  number  of  switches 
or  contactors,  which  close  and  open  the  various  motor, 


RAILWAY  MOTOR   CONTROL.  105 

resistance,  or  compensator  circuits,  and  in  general  effect 
the  changes  in  connection  necessary  in  controlling  the 
particular  type  of  motor  employed.  Each  of  these  con- 
tactors opens  in  a  strong  magnetic  field,  so  that  all  arcs  are 
immediately  disrupted.  A  separate  reversing  switch  gov- 
erns the  direction  of  rotation  of  the  motors.  On  motor  cars 
all  this  apparatus  is  usually  placed  underneath  the  car, 
but  on  locomotives  it  is  located  in  the  cab.  The  contac- 
tors and  reverser  may  be  operated  by  solenoids  or  by  the 
use  of  compressed  air  controlled  by  electrically  operated 
valves.  In  either  case  the  solenoids  or  other  electromag- 
nets that  govern  the  movement  of  the  switches  are  connected 
to  the  wires  of  the  auxiliary  circuit  and  are  supplied  with 
current  in  proper  sequence  by  the  hand-operated  master 
controller. 

The  master  controller  is  considerably  smaller  than  the 
ordinary  street-car  controller,  but  is  similar  in  appearance 
and  method  of  operation.  The  contact  fingers  of  each 
master  controller  are  connected  to  the  wires  of  the  auxiliary 
or  control  circuit,  which  usually  consists  of  a  multiple- 
conductor  cable.  By  means  of  suitable  couplers  this  con- 
trol cable  is  made  continuous  throughout  any  number  of 
motor  cars  or  locomotives  operated  together  in  a  train. 
Current  for  the  master  control  is  taken  from  the  line,  or 
from  a  storage  battery,  through  whichever  master  controller 
the  motorman  operates.  Since  this  current  is  used  solely 
for  energizing  the  operating  coils  of  the  motor  contactors, 
its  value  is  comparatively  small,  usually  not  exceeding 
2.5  amperes  for  each  car  equipment.  As  the  operating 
coils  of  each  motor  controller  are  connected  to  the  wires 
of  the  control  cable,  any  master  controller  on  the  train 
will  simultaneously  operate  corresponding  contactors  on 


io6 


TRACTION  AND   TRANSMISSION. 


all  the  motor  cars  and  thus  establish  similar  motor  con- 
nections on  them.  To  avoid  accidents  which  may  occur 
through  the  physical  disability  of  a  motorman,  the  operat- 
ing handle  of  the  master  controller  is  sometimes  provided 
with  a  button  which  must  be  held  down  in  order  to  keep 
the  auxiliary  control  circuit  closed.  In  some  cases  the  con- 
nections are  so  arranged  that  releasing  this  button  applies 
the  air  brakes  as  well  as  opens  the  control  circuits. 


Fig.  48. 

The  essential  features  of  the  multiple-unit  system  of 
control  as  applied  to  direct-current  equipments  are  illus- 
trated in  Fig.  48,  which  shows  the  principal  motor  and 
control  circuits  for  one  motor  car.  For  clearness  the  re- 
verser  is  omitted,  as  are  also  the  circuits  necessary  for  its 
control.  Assuming  therefore  that  the  reverser  is  properly 
set,  the  subsequent  operation  of  the  control  system  during 
initial  acceleration  is  as  follows:  turning  one  of  the  master 
controllers  to  the  first  notch  results  in  the  closing  of  contac- 


RAILWAY  MOTOR   CONTROL.  107 

a,  b,  and  h,  due  to  current  received  from  train  wires  i, 
2,  and  8,  thus  establishing  connection  with  the  line  and 
placing  the  two  motors  and  a  protecting  resistance  in 
series.  Turning  the  master-controller  handle  successively  to 
notches  2,  3,  and  4  closes  contactors  c,  d,  and  e,  respectively, 
thereby  progressively  reducing  the  resistance  by  placing 
additional  resistance  units  in  parallel.  When  the  controller 
handle  is  moved  to  the  fifth  notch,  contactor  /  is  closed, 
short-circuiting  the  resistances  and  connecting  the  motors 
in  series  across  the  line.  In  passing  over  the  sixth  or  tran- 
sition notch  contactors  c  to  /  and  h  are  opened,  followed  by 
the  closing  of  contactors  g  and  i.  This  places  the  motors 
in  parallel,  with  resistance  in  series  with  both.  Turning 
the  master-controller  handle  successively  to  notches  7,  8, 
9,  and  10  progressively  reduces  the  resistance  as  before 
until  each  motor  is  operating  on  full  line  voltage. 

The  operation  of  the  switches  of  a  multiple-unit  equip- 
ment in  other  than  their  proper  sequence  is  prevented  by 
various  interlocking  devices.  For  example,  the  connec- 
tions are  so  arranged  that  the  reverser  on  a  car  cannot  be 
actuated  save  when  the  contactors  on  that  car  are  open,  nor 
can  the  operating  coils  of  the  contactors  be  energized  unless 
the  reverser  is  properly  set  for  the  direction  of  motion  indi- 
cated by  the  master  controller.  By  means  of  a  suitable 
cut-out  switch  the  operating  coils  of  the  motor  controller 
on  any  car  can  be  disconnected  from  the  control  circuit 
without  interfering  with  the  operation  of  the  train  from 
either  of  the  master  controllers  on  that  car. 

In  multiple-unit  equipments  similar  to  that  illustrated 
in  Fig.  48  the  progressive  closing  of  the  contactors  is 
accomplished  by  turning  the  master-controller  handle  to 
successive  notches.  The  maintenance  of  an  approximately 


108  TRACTION  AND  TRANSMISSION. 

constant  current  during  initial  acceleration  is  therefore 
entirely  dependent  on  the  motorman's  care  and  skill.  It 
is  often  desirable  to  have  the  progressive  operation  of  the 
contactors  regulated  by  the  motor  current  itself,  in  order 
that  the  variations  in  this  current  from  the  average  value 
required  during  acceleration  may  be  automatically  re- 
stricted to  the  prescribed  range,  thereby  insuring  a  uniform 
rate  of  acceleration  and  permitting  the  motorman  to  con- 
fine his  attention  to  the  track  and  signals.  This  auto- 
matic acceleration  is  effected  by  means  of  current-limit 
relays  having  coils  connected  in  series  with  the  motor  cir- 
cuit. Such  relays  may  be  arranged  to  regulate  the  pro- 
gressive closing  of  the  motor-controller  switches  in  either 
of  two  ways :  i ,  by  governing  the  movement  of  the  master- 
controller  contact  cylinder,  or  2,  by  governing  the  supply  of 
current  to  the  operating  coils  of  the  individual  contactors. 

In  the  former  method  the  contact  cylinder  of  each  master 
controller  is  connected  to  its  operating  handle  through  a 
helical  spring.  The  cylinder  is  restrained  by  a  magnetic 
clutch  actuated  by  a  current  relay  in  series  with  the  motor 
circuit.  This  relay  is  so  adjusted  as  to  release  the  clutch 
and  allow  the  contact  cylinder  to  advance  one  step  whenever 
the  motor  current  falls  to  its  minimum  limiting  value.  The 
master-controller  handle  may  therefore  be  turned  at  once 
to  any  desired  position,  and  the  contact  cylinder  will 
follow  in  successive  steps  automatically  governed  by  the 
motor  current  of  the  car  on  which  the  motorman  is  stationed. 
Evidently  this  method  cannot  be  expected  to  give  satis- 
factory results  in  cases  where  there  is  a  material  difference 
in  the  motor  characteristics  or  the  current  requirements  of 
the  various  cars  composing  a  train. 

In  the  second  method  of  automatic  acceleration  each 


RAILWAY  MOTOR   CONTROL.  109 

motor  car  is  provided  with  a  current-limit  relay  that  is 
designed  and  adjusted  with  reference  to  the  requirements 
of  that  particular  car  equipment.  The  motor  connection 
ultimately  established  on  all  the  motor  cars  in  a  train  is 
determined  by  the  position  to  which  the  handle  of  the 
master  controller  is  turned;  but  the  successive  steps  neces- 
sary to  attain  this  connection  are  governed  independently 
for  each  car  by  the  motor  current  of  that  car.  The  connec- 
tions between  the  operating  coils  of  the  contactors  and  the 
control  circuit  are  made  automatically  through  auxiliary 
contacts  on  the  contactors  themselves;  and  the  control 
current  for  closing  these  switches  passes  through  the  con- 
tacts of  the  current-limit  relay. 

PROBLEMS. 

19.  Determine  the  resistance  units  of  a  rheostatic  railway  controller  for 
use  with  one  35-horsepower,  500- volt,  direct-current  motor  having  a  resist- 
ance of  1. 1 8  ohms.     The  saturation  curve  of  the  motor  is  shown  in  Fig.  39. 
The  average  current  required  during  initial  acceleration  is  50  amperes;  and 
the  maximum  and  minimum  values  of  the  current  must  not  differ  from  this 
average  value  by  more  than  9  %. 

20.  Determine  the  parallel  resistance  steps  of  a  series-parallel  railway 
controller  for  use  with  two  35-horsepower,  soo-volt,  direct-current  motors, 
the  saturation  curves  of  which  are  shown  in  Fig.  39,  the  resistance  of  each 
motor  being  1.18  ohms.      An  average  current  of  50  amperes  per  motor  is 
required  during  uniform  acceleration,  and  the  limiting  values  of  current 
are  specified  at  45  and  55  amperes. 

21.  A  2  20- volt,  single-phase  motor  is  to  be  started  by  means  of  an  induc- 
tion regulator  with  an  initial  voltage  of  150.     What  are  the  angular  dis- 
placements between  the  two  regulation  coils  if  7  steps  were  required  which 
yield  equal  voltage  increments  on  the  motor  ? 

22.  Determine  the  resistance  and  the  inductance  of  a  preventive  coil  to 
be  connected  in  series  with  a  certain  compensator  switch  in  order  to  effect 
sparkless  transition  by  the  method  of  control  illustrated  in  Fig.  41.     At 
the  instant  during  acceleration  when  this  particular  switch  is  to  be  closed 
the  25-cycle  motors  have  attained  a  speed  such  that  the  power  factor  of 
the  motor  circuit  is  53  %,    The  motor  current  during  the  period  of  initial 


110  TRACTION   AND  TRANSMISSION. 

acceleration  is  approximately  constant  at  100  amperes  and  the  E.M.F. 
between  adjacent  compensator  taps  is  25  volts. 

23.  A  motor  car  is  equipped  with  four  three-phase,  four-pole  induction 
motors  arranged  in  pairs  for  cascade  control.  Each  main  motor  has  5 
stator  slots  per  pole  per  phase  and  18  conductors  per  primary  slot.  Each 
auxiliary  motor  has  4  stator  slots  per  pole  per  phase  and  4  conductors  per 
primary  slot.  Determine  the  equivalent  number  of  stator  conductors  per 
pole  when  the  motors  are  operating  in  cascade. 


ENERGY    CONSUMPTION.  Ill 


CHAPTER   VI. 

ENERGY   CONSUMPTION. 

37.  Current  Curves.  —  During  the  period  of  initial  accel- 
eration of  a. car  the  current  taken  by  the  direct-current 
motors  is  maintained  roughly  constant  by  the  control 
equipment,  provided  no  changes  of  grade  or  curvature 
occur  during  this  interval.  Thereafter,  until  the  car  attains 
its  ultimate  uniform  velocity  on  the  particular  roadway 
under  consideration,  the  motor  current  decreases,  at  first 
rapidly  and  later  more  slowly.  The  instantaneous  values 
of  current  from  the  time  all  the  controller  resistance  is 
cut  out  until  the  power  is  shut  off  may  be  read  directly 
from  the  performance  curves  of  the  motor,  since  each  motor 
takes  a  definite  current  at  the  various  speed  values  of  the 
car  during  this  period.  A  curve  showing  these  instantane- 
ous current  values  in  terms  of  time  over  a  run  is  called  a 
current  curve  of  the  railway  motor,  and  serves  as  the  basis 
for  determining  whether  the  assumed  motor  for  a  proposed 
installation  can  perform  the  prescribed  service  without 
overheating. 

It  is  usual  to  construct  the  curve  of  current  per  car 
rather  than  the  current  per  motor  in  determining  the 
energy  consumption  of  a  tentative  equipment.  When 
starting  the  car  the  two  motors  of  a  two-motor  direct- 
current  equipment  are  connected  in  series,  or  the  four 
motors  of  a  four-motor  equipment,  arranged  for  the  usual 
series-parallel  control,  are  connected  in  two  groups  joined 


112  TRACTION  AND   TRANSMISSION. 

in  series,  each  group  consisting  of  two  motors  connected 
in  parallel.  Four-motor  equipments  adapted  for  series, 
series-parallel,  parallel  control  are  not  frequently  employed. 
Hence  from  the  instant  of  starting  until  the  controller 
leaves  the  series  position  and  connects  all  the  motors  in 
parallel  with  resistance  across  line  voltage  the  current  per 
car  is  equal  to  the  current  per  motor  times  one-half  the 
number  of  motors  comprising  the  car  equipment.  At  the 
end  of  this  period,  that  is,  when  the  motors  are  operating 
on  the  series  position  without  resistance,  the  speed  of  the 
car  is 


where  E  is  the  line  voltage,  /  is  the  current  traversing  the 
motor  and  R  is  its  resistance,  and  Vi  is  the  car  speed  when 
the  controller  is  full  "on."  It  is  at  this  speed  that  the 
current  per  car  increases  from  its  former  value  to  the 
product  of  the  current  per  motor  times  the  number  of 
motors  on  the  car.  While  the  motors  operate  on  reduced 
voltage  in  the  parallel  position  their  current  intake  is  con- 
stant, but  thereafter  the  current  per  motor  and  that  per  car 
decrease  as  dictated  by  the  motor  performance  curves  on 
full  line  voltage.  When  coasting  begins  the  current  intake 
ceases  and  the  current  curve  drops  to  zero. 

38.  Average  and  Effective  Currents.  —  The  average  cur- 
rent taken  by  the  car  over  a  complete  run  is  based  not 
merely  upon  the  time  during  which  the  car  receives  power 
for  propulsion  nor  upon  the  running  time,  but  upon  the 
time  of  the  entire  run  including  stops.  This  average 
current  is  determined  by  finding  the  area  of  the  current 


ENERGY   CONSUMPTION.  113 

curve  and  dividing  it  by  the  time  of  the  run  as  given  by 
the  specified  schedule  speed. 

The  current  per  motor  which  when  flowing  continuously 
will  yield  the  same  average  copper  loss  in  the  windings  is 
called  the  effective  motor  current  and  is  equal  to  the  square 
root  of  the  average  of  the  squares  of  the  instantaneous 
current  values.  The  effective  current  may  be  found  by 
squaring  a  suitable  number  of  values  of  the  motor  current 
and  plotting  these  squared  values  on  the  time  axis.  The 
square  root  of  the  average  ordinate  of  the  curve  drawn 
through  these  points  and  taken  over  the  total  time  of  run 
represents  the  equivalent  motor  current  to  which  the  heat- 
ing of  the  machine  is  proportional. 

39.  Numerical  Example.  —  As  an  illustration,  consider 
a  car  equipped  with  .four  5o-horsepower,  6oo-volt,  G.E. 
2i6-A  direct-current  motors  whose  characteristic  curves 
are  shown  in  Fig.  23.  The  speed  curve  of  this  car  over  an 
0.8  mile  run  on  a  straight  level  track  at  a  schedule  speed  of 
20  miles  per  hour  is  shown  in  Fig.  31,  which  permits  of  a 
2o-second  stop.  Determine  (i)  the  average  current  intake 
for  the  car  and  (2)  the  effective  current  per  motor. 

The  current  consumed  by  the  motor  as  the  car  is  accel- 
erated uniformly  at  1.5  miles  per  hour  per  second  from 
standstill  to  a  speed  of  16.9  miles  per  hour  (see  page  61) 
is  maintained  roughly  constant  at  a  mean  value  of  64 
amperes,  the  time  necessary  for  the  acquirement  of  this 
speed  being  11.3  seconds.  The  current  curve  over  this 
period  will  have  a  series  of  peaks  occasioned  by  the  vari- 
ations in  voltage  which  is  impressed  upon  the  motors  by 
the  controller,  but  the  exact  shape  of  this  part  of  the  curve 
is  of  no  particular  consequence,  and  it  may  be  drawn 
straight  through  the  mean  current  value.  Taking  the 


TRACTION  AND  TRANSMISSION. 


resistance  of  each  motor  as  0.30  ohm,  the  resistance  drop 
thereof  is  19.2  volts.  Therefore  the  speed  of  the  car  at 
the  instant  when  the  transition  from  the  series  to  the 
parallel  position  is  made. is 

600 

—  -  19.2 

X  16.9  =  8.2  miles  per  hour. 


600  —  19.2 


8.2 


This  speed  is  attained  in  -  -  =  5.46  seconds  from  the  instant 

of  starting.  Thus,  when  the  car  is  in  motion  for  5.46  seconds 
the  current  per  car  increases  from  64  X  I  or  128  amperes 
to  64  X  4  or  256  amperes.  The  latter  current  value  per- 
sists for  11.3  —  5.46  or  5.84  seconds.  The  current  curve 
for  the  car  before  the  motors  operate  on  full  line  voltage  is 
shown  by  OABCD  in  Fig.  49. 

Beyond  the  point  D  the  current  curve  is  entirely  depen- 
dent upon  the  motor  performance  curves,  since  the  current 
intake  per  motor  at  different  car  speeds  is  directly  obtain- 
able therefrom.  The  times  at  which  these  speeds  obtain 
are  given  by  the  speed  curve  for  the  run  under  consider- 
ation. Thus  the  curve  of  current  per  car  may  be  plotted 
in  terms  of  time,  as  done  herewith  from  the  following  com- 
putations: 


Speed  of  car 
(miles  per  hour). 

Current  per  motor 
(amperes). 

Current  per  car 
(amperes). 

Time  of  speed  acquire- 
ment (seconds).     See 
table,  page  64. 

20 

48.2 

192.  8 

13-84 

22 

42.1 

168.4 

16.26 

24 

37-4 

149.6 

19-45 

26 

33-9 

135-6 

23-65 

28 

31.0 

124.0 

29.22 

30 

28.4 

113.6 

36.88 

32 

26.3 

105.  2 

47.78 

ENERGY   CONSUMPTION. 


8 


o  o 

o  o 

CO  ^~ 

S±TOA 


Il6  TRACTION  AND    TRANSMISSION, 

After  50  seconds  coasting  begins  and  the  current  curve 
is  completed  by  drawing  the  vertical  line  EF. 

The  area  of  the  current  curve  per  car  is  7350  ampere- 
seconds,  which  when  divided  by  the  time  of  the  run,  namely 
144  seconds,  gives  the  average  current  per  car  over  the 
given  run  as  51.0  amperes. 

The  curve  of  current  per  motor  is  shown  in  Fig.  50, 
as  OABCD,  the  portion  BC  being  also  plotted  from  the 
values  recorded  in  the  foregoing  table.  The  ordinates  of 
this  curve  when  squared  yield  the  curve  OEFGD,  the  area 
of  which  is  90,930  ampere2-seconds.  The  mean  square 
current  over  the  given  run  which  requires  144  seconds  for 
its  completion  is  631  (amperes)2.  Therefore  the  effective 
heating  current  of  the  motor  is  25.1  amperes. 

40.  Effective  Motor  Current  for  a  Trip.  —  The  effective 
motor  current  for  a  trip  over  an  entire  roadway  which  is 
divided  into  a  number  of  individual  runs  distributed  over 
several  territorial  sections  on  which  different  service  condi- 
tions exist  is  obtained  by  averaging  the  squared  current 
values  over  all  the  runs  and  extracting  the  square  root  of 
this  average.  Thus,  for  example,  if  the  effective  motor 
current  values  on  typical  runs  on  the  city,  suburban,  and 
interurban  sections  of  a  certain  railway  are  respectively 
40  amperes  for  25  minutes,  35  amperes  for  20  minutes, 
and  28  amperes  for  15  minutes,  then  the  effective  current 
for  the  entire  trip  is 


(40*  X  25)  +  (35*  X  20)  +  (282  X  15) 
25  +  20+  15 


,  / 40,000  +  24,500  +11,760  =       6 

V  Art  35-  ' 


ENERGY    CONSUMPTION. 


117 


o  z 

000 


Il8  TRACTION  AND  TRANSMISSION. 

since  this  current  flowing  for  60  minutes  would  produce  the 
same  heating  of  the  motor  as  is  developed  under  the  actual 
service  conditions. 

41.  Voltage  Curve.  —  The  line  voltage  in  calculations 
of  motor  capacity  is  assumed  constant  and  to  have  the 
same  value  everywhere  on  the  roadway.     The  voltage  on 
the  motor  equipment  is  thus  considered  constant,  and  a 
voltage  curve  would  be  a  straight  horizontal  line,  as  OMNF 
in    Fig.    49.     The    voltage    impressed    upon    the    motor 
terminals    during    the    period    of    initial    acceleration    is 
increased  from  zero  to  full  line  voltage  in  steps  by  means 
of  the  controller.     As  a  rule  there  are  more  than  seven 
such  steps,  the  usual   minimum  representing  four  series 
resistance  steps  and  three  parallel  resistance  steps  in  the 
control  apparatus.     The  actual  voltage  variations  are  of  no 
consequence, -and  the  voltage  per  motor  may  with  sufficient 
accuracy  be  considered  as  uniformly  increased  from  zero 
to  its  final  value.     The  motor  voltage  would  then  be  repre- 
sented by  a  curve  as  OPQD  in  Fig.  50,  the  point  P  indicat- 
ing the  time  when  the  controller  is  full  on. 

42.  Motor  Heating.  —  To  ascertain  whether  a  motor  is 
suited  for  a  proposed  railway  service,  the  conditions  of  that 
service  must  be  investigated  as  already  outlined.     Barring 
commutation  limitations,  the  motor  must  be  large  enough 
to  dissipate  the  heat  occasioned  by  the  copper  and  iron 
losses  without  excessive  temperature  elevation.     The  cop- 
per loss  over  a  typical  run  is  equal  to  the  product  of  the 
square  of  the  effective  motor  current  and  the  resistance 
of  the  motor  windings.     The  iron  loss  depends  upon  the 
magnetic  flux  density  of  the  iron  and  the  armature  speed. 
These  rrTfurn  depend  upon  the  current  and  upon  the  vol- 
tage impressed  upon  the  motor  terminals.     If  iron  loss 


ENERGY   CONSUMPTION.  1 19 

curves  of  the  motor,  for  various  current  strengths,  plotted 
in  terms  of  motor  impressed  E.M.F.  be  available,  a  curve 
of  iron  loss  for  the  time  during  which  the  power  is  on  the 
motor  can  be  constructed,  since  at  each  instant  of  time  the 
motor  current  and  voltage  are  known.  Having  subse- 
quently determined  the  average  ordinate  of  such  an  iron 
loss  curve  over  the  entire  run,  that  voltage  may  be  found 
which,  with  the  effective  motor  current,  will  yield  the 
same  total  iron  loss.  Thus,  to  reproduce  the  heating  con- 
ditions of  a  proposed  service  in  a  shop  test,  it  is  only  nec- 
essary to  operate  the  motor  for  a  sufficient  time  with  the 
effective  motor  current  value  which  gives  the  average  cop- 
per loss  at  that  voltage  which  gives  with  this  current  value 
the  average  iron  loss.  Such  continuous  operation  should 
not  result  in  a  greater  temperature  rise  than  75°  C.,  start- 
ing cold.  Should  the  calculations  relating  to  -a  tentative 
equipment  indicate  a  greater  temperature  elevation  than 
this  the  motors  must  be  discarded  and  a  new  set  of  cal- 
culations based  upon  larger  units  must  be  made. 

The  equivalent  voltage  on  500  to  600  volt  direct-current 
motors  which  yields  the  average  iron  loss  does  not  vary 
widely  and  is  generally  somewhat  less  than  250  volts  and 
rarely  exceeds  350  volts  even  on  interurban  service  with 
infrequent  stops.  Therefore,  if  the  continuous  capacity 
of  a  railway  motor  is  stated  in  terms  of  the  current  which 
it  can  carry  with  a  75°  C.  temperature  rise  at  both  300  volts 
and  400  volts,  an  accurate  idea  of  its  suitability  for  a  pro- 
posed service  can  be  inferred.  This  is  the  present  method 
used  by  the  Westinghouse  Company  of  rating  railway 
motors.  The  nominal  horsepower  rating  so  frequently 
given  serves  as  an  indication  of  the  commutating  limits 
and  mechanical  strength  of  the  motor;  it  is  usually  based 


120  TRACTION  AND  TRANSMISSION. 

on  a  one-hour  test  with  that  load  which  gives  a  tempera- 
ture rise  of  75°  C.  above  the  surrounding  air  taken  as  25° 
C.  at  the  end  of  that  period. 

43.  Energy  for  Direct-current  Propulsion.  —  The  energy 
required  for  the  propulsion  of  cars  operating  on  direct 
current  may  be  derived  from  the  current  and  voltage  curves 
of  the  motor  equipment.  The  watts  input  to  a  car  at  any 
instant  is  equal  to  the  line  voltage  times  the  instantaneous 
current  per  car.  Thus  a  curve  of  power  input  can  be  plotted 
in  terms  of  time.  The  area  of  this  power  curve  would 
represent  the  electrical  energy  consumed  during  the  run. 

Having  already  determined  the  average  current  per  car 
in  the  foregoing  numerical  illustration  over  a  particular 
run,  namely  51  amperes,  it  is  only  necessary  to  multiply 
this  value  by  the  line  voltage  and  by  the  total  time  of  the 
run  to  obtain  the  energy  consumption.  Thus  the  electrical 
energy  consumed  is 

51  X  600  X  144=  4,410,000  watt-seconds, 
=         1,225  watt-hours, 
=         1.225  kilowatt-hours. 

In  order  to  effect  comparisons  between  different  equip- 
ments as  to  economy  of  operation  the  energy  consumed  must 
be  based  upon  some  definite  distance,  such  as  a  one-mile 
run.  Energy  consumption  in  kilowatt-hours  per  car-mile 
serves  as  a  fair  basis  of  comparison  for  cars  weighing  approx- 
imately the  same  but  operating  at  different  schedule  speeds. 
When  the  car  weights  also  differ  considerably,  the  basis  of 
comparison  should  be  the  energy  in  watt-hours  per  ton-mile. 

In  the  particular  case  of  the  24.32  ton  car  making  the 
0.8  mile  run  under  consideration,  the  energy  consumed  may 
be  expressed  as 


ENERGY  CONSUMPTION.  121 

1.22^ 

or 


—  1.53  kilowatt-hours  per  car-mile, 
0.8 


T  o  *y  £ 

^ —  =  6^  watt-hours  per  ton-mile. 

0.8  X  24.32 

44.  Energy  for  Alternating-current  Propulsion.  —  Be- 
cause of  the  varying  power  factor,  the  calculation  of  energy 
consumption  of  alternating-current  railway  equipments  is 
not  as  simple,  as  for  the  direct-current  equipments  so  far 
discussed.  The  process  of  constructing  current  curves  for 
the  portion  of  the  run  after  the  period  of  constant  accel- 
eration, that  is,  when  full  voltage  is  impressed  upon  the 
motors,  is  exactly  the  same  as  for  direct-current  equipments. 
The  initial  portion  of  the  current  curve,  which  refers  to 
the  current  intake  while  the  car  is  accelerated  uniformly, 
is,  however,  difficult  of  exact  determination  in  the  case  of 
alternating-current  railway  apparatus.  The  current  taken 
by  a  single-phase  motor  increases  somewhat  during  the 
period  of  constant  acceleration,  then  decreases  again  before 
the  expiration  of  this  period,  as  shown  by  the  curve  in 
Fig.  51.  In  this  figure  are  shown  curves  of  speed,  total 
motor  current,  volts  on  motor,  and  motor  power  factor, 
which  were  obtained  by  test  with  a  50- ton  car,  e'quipped 
with  four  7 5 -horsepower,  single-phase  motors,  over  a  two- 
mile  run. 

In  the  absence  of  such  experimental  data,  the  current 
taken  by  the  motors  of  a  proposed  equipment  for  the 
period  of  uniform  acceleration  may  be  assumed  constant 
at  the  value  corresponding  to  the  speed  at  which  the  rate 
of  acceleration  diminishes.  On  this  assumption  the  current 
curve  would  have  the  form  OABC,  the  portion  BC  being  de- 
termined from  the  motor  performance  curves  corresponding 


122  TRACTION  AND  TRANSMISSION. 

to  the  various  speed  values.  The  average  motor  current,  or 
the  effective  current  over  the  run,  is  then  readily  obtainable. 

Since  the  voltage  impressed  upon  an  alternating-current 
series  motor  at  the  first  controller  notch  is  usually  about 
one-half  of  its  final  value,  no  great  error  will  be  introduced 
in  the  calculation  of  energy  consumption  by  assuming  that 
the  motor  voltage  increases  from  the  above-mentioned  start- 
ing value  uniformly  to  its  maximum  value.  Thus,  in  Fig.  5 1 , 
the  actual  voltage  curve  HG  may  with  sufficient  exactness 
be  replaced  by  the  curve  EFG.  The  average  motor  voltage 
may  in  this  way  be  found  without  a  knowledge  of  the 
experimental  irregular  curve. 

By  making  these  two  assumptions  regarding  the  form  of 
those  portions  of  the  current  and  voltage  curves  which 
correspond  to  the  period  of  uniform  acceleration  of  the  car, 
the  power  taken  by  motors  may  be  computed  in  kilovolt- 
amperes.  The  power  factor  of  alternating-current  railway 
motors  on  full  voltage  at  different  current  inputs  is  em- 
bodied in  the  performance  curves  thereof.  On  the  lower 
motor  voltages  during  the  period  of  initial  acceleration  the 
power  factor  is  low.  Its  value  during  this  time  may  be  con- 
sidered as  increasing  uniformly  to  its  value  at  full  voltage, 
with  the  supposedly  constant  accelerating  current,  from  a 
value  at  starting  equal  to  about  40  %  of  its  value  at  the 
instant  when  full  voltage  is  applied  to  the  motors.  Thus, 
the  actual  power-factor  curve  of  the  motors  shown  as  PMN 
in  Fig.  51  may  be  represented  by  the  curve  LMN.  This 
assumption  makes  possible  the  calculation  of  the  power 
input  to  the  motors  in  kilowatts.  The  total  energy  con- 
sumption of  the  equipment  may  be  obtained  by  adding 
to  this  motor  input  the  losses  in  the  compensators,  trans- 
formers, and  car  wiring. 


ENERGY   CONSUMPTION. 


I23 


g        X  <  UJ    g  JO. 

•anoH  a3d  S31IW 


S 
1N30  U3d 


124  TRACTION  AND   TRANSMISSION. 

45.  Effect  of  Operating  Conditions  on  Energy  Consump- 
tion. —  In  order  to  determine  the  effect  on  the  energy 
consumption  of  a  railway  equipment  when  the  operating 
conditions  are  changed,  such  as  altering  the  initial  rate  of 
acceleration,  the  length  of  run,  the  number  and  duration 
of  stops,  the  gear  ratio,  the  braking  rate,  and  the  line 
voltage,  it  is  necessary  to  consider  how  the  total  energy 
taken  from  the  trolley  or  third  rail  is  expended.  The  energy 
supplied  to  a  car  or  train  during  acceleration  changes  the 
momentum  thereof,  and  the  greater  part  of  this  energy  ap- 
pears in  the  kinetic  form,  the  remainder  being  expended 
in  overcoming  train  resistance  and  in  heating  the  starting 
rheostats  and  motor  circuits.  In  bringing  the  car  to  rest 
subsequently  the  kinetic  energy  must  be  dissipated.  Left  to 
itself,  the  car  would  continue  to  move  until  all  its  energy 
of  motion  is  lost  in  overcoming  train  resistance,  and  if,  as 
is  the  usual  case,  the  car  is  quickly  brought  to  standstill 
after  coasting  for  a  time,  the  greater  portion  of  the  kinetic 
energy  is  consumed  in  heating  the  brake  shoes  and  car 
wheels.  Thus,  the  energy  supplied  to  railway  equipments 
is  the  sum  of  (a)  the  energy  required  to  overcome  the  train 
resistance  throughout  the  entire  run,  (b)  the  energy 
wasted  in  the  starting  rheostats,  motors,  and  car  wiring, 
and  (c)  the  energy  consumed  in  braking. 

A  slight  reduction  in  train  resistance  such  as  might  be 
effected  by  the  employment  of  ball  or  roller  bearings  in 
diminishing  bearing  friction,  permits  of  a  higher  rate  of 
acceleration  with  the  same  motor  current.  The  greater 
the  acceleration  rate  the  more  coasting  is  possible  on  a 
given  run  for  the  same  schedule  speed  and  the  shorter  is 
the  time  during  which  the  motors  receive  power.  A  con- 
siderable saving  of  energy  may  result  from  the  reduction 


ENERGY    CONSUMPTION. 


125 


of  train  resistance  to  a  minimum.  With  a  given  equipment 
the  energy  expended  in  overcoming  train  resistance  is 
approximately  constant  for  a  given  run. 

The  energy  lost  in  the  starting  resistances  is  proportional 
to  the  time  that  these  devices  carry  current.  The  losses 
in  the  car  wiring  are  usually  small  enough  to  be  neglected 
in  considerations  of  this  kind.  The  motor  iron  losses  and 
the  loss  in  the  gears  are  practically  constant  over  the  period 
during  which  the  power  is  on.  The  copper  loss  in  the  motors 


0.5 


1.0  1.5  2.0 

MILES  PER  HOUR  PER  SECOND 

Fig.  52. 


2.5 


3.0 


is  proportional  to  the  square  of  the  current,  and  therefore 
the  higher  rates  of  acceleration  with  the  accompanying 
larger  currents  result  in  a  greater  loss  and  consequent 
increase  of  heating  in  the  motors.  On  the  other  hand, 
increased  acceleration  implies  a  shorter  time  during  which 
the  motors  receive  energy,  and  therefore  tends  to  reduce 
heating.  These  two  opposing  conditions  suggest  that  there 
is  a  definite  rate  of  acceleration  which  will  yield  a  minimum 
heating  in  a  given  case. 


126 


TRACTION  AND   TRANSMISSION. 


The  energy  consumed  in  braking  depends  upon  the  brak- 
ing rate  and  upon  the  speed  of  the  car  when  the  brakes 
are  applied.  More  coasting  is  permissible  on  a  given  run 
when  high  braking  rates  are  employed,  and  the  car  speed 
at  which  braking  begins  is  lower.  Braking  immediately 
after  turning  off  the  power  and  thus  bringing  the  car  to 
rest  slowly  results  in  inefficient  operation. 

The  curves  of  Fig.  52  show  the  motor  current  during  the 
period  of  initial  acceleration,  the  time  of  running  on  resist- 
ance, and  the  speed  of  the  car  at  the  instant  of  full- voltage 
application  to  the  motors,  in  terms  of  the  acceleration  rates, 
for  the  24.32-ton  car  already  mentioned,  which  is  equipped 
with  four  5o-horsepower,  direct-current  motors.  These 
curves  are  plotted  from  the  following  data  taken  from  the 
characteristic  curves  of  the  motors,  Fig.  23. 


Acceleration 
rate. 

Total  tractive 
effort  per 
motor. 

Accelerating 
current. 

Speed  at  full  voltage 
with  initial  accel. 
current. 

Running  time 
on  resistance. 

•25 

222 

27.0 

31-8 

127.2 

•5 

374 

34-7 

25-5 

51-0 

•75 

526 

42.2 

22.  O 

29.4 

I.O 

678 

49-5 

IQ.7 

19.7 

1-25 

830 

56.3 

18.1 

14-5 

i-5 

982' 

64.0 

16.9 

n-3 

i-7S 

H34 

70.6 

16.0 

9.1 

2.O 

1286 

77-7 

15.2 

7.6 

2.25 

1438 

85.0 

*4-5 

6-5 

(Train  resistance  taken  as  70  pounds.) 

The  curves  verify  the  foregoing  general  statement  that 
the  .greater  the  rate  of  acceleration  the  larger  will  be  the 
current  during  uniform  acceleration  of  the  car  but  the 
shorter  will  be  the  time  during  which  this  current  flows; 
and  they  show  the  dependence  of  these  factors  upon  the 
rate  of  acceleration  for  this  particular  equipment.  The 


ENERGY   CONSUMPTION. 


127 


maximum  schedule  speed  possible  on  any  given  run  is  a 
direct  function  of  the  rates  of  acceleration  and  braking. 

The  maximum  possible  schedule  speed  increases  with 
larger  runs,  provided  all  other  conditions  remain  unaltered. 
Thus,  in  the  case  of  the  24. 3 2-ton  car  to  which  frequent 
reference  is  made,  the  relation  between  maximum  schedule 
speed  and  the  length  of  the  run  on  level  track,  allowing  for 


0.5 


1.0 


1.5 
MILES  RUN 

Fig.  53- 


2.0 


2.5 


3.0 


2o-second  stops  but  no  coasting,  is  shown  in  Fig.  53.  This 
curve  is  based  on  data  obtained  from  Fig.  31,  on  which  a 
number  of  braking  curves  may  be  drawn  corresponding  to 
runs  of  various  lengths. 

Proportionately  less  of  the  energy  taken  from  the  supply 
circuit  is  used  to  overcome  the  losses  in  other  than  train 
resistance  for  long  runs  than  in  short  runs,  and  therefore 
the  power  consumption  per  mile  is  decreased  by  increasing 
the  lengths  of  runs.  This  is  also  shown  in  Fig.  53  for  the 
particular  car  under  consideration;  the  curve  of  power  con- 
sumption per  car  mile  without  coasting  was  computed  in 


128 

50 

40 

1-30 

z 

LJ 
O 
£E 
£20 

10 

TRACTION   AND   TRANSMISSION. 

^ 

^ 

6-CARTRAIN.-4  MOTOR  CARS.-1  54 
TONS.  AVG.  BRAKING  RATE1.  75       v' 
MILES  PER  HR.  PER  SEC.  STATIONX*/ 
STOP-1  2  SECONDS.               x°/    , 

^ 

•^ 

i 

oVy 
o// 

i: 

y 

Off 

Kf 

,*[ 

0.5  1.0  1.5  2.0 

RATE   OF  ACCELERATION  IN  MILES  PER  HOUR  PER  SECOND. 
Fig.  54- 


40 


Id 
O 

cc 

Lit 

0.20 


6  CAR  TRAIN.  4  MOTOR  CARS,  154 

TONS.  ACCELERATION  1.33, 

MILES  PER  HOUR  PER  SECOND, 

STATION  STOP  10  SECONDS. 


0.5  I.O  1.5  2.0 

RATE  OF  BRAKING  IN  MILES  PER  HOUR  PER  SECOND 
Fig.  55. 

connection  with  Fig.  49.  The  effect  on  schedule  speed  and 
on  energy  consumption  of  changes  in  the  rates  of  accelera- 
tion and  braking  is  not  as  conspicuous  on  long  runs  as 
on  short  ones. 


ENERGY  CONSUMPTION. 


129 


The  schedule  speed  of  railway  cars  depends  to  a  great 
extent  upon  the  duration  of  the  stops  for  the  purpose  of 
taking  on  or  discharging  passengers  or  freight.  Obviously, 
the  longer  the  period  of  standstill  the  lower  will  be  the 
maximum  schedule  speed  attainable  by  a  given  equipment. 

An  increase  in  the  time  of  coasting  results  in  a  reduction 
of  the  power  consumption.  The  results  of  a  series  of  recent 


50 


40 


H30 

hi 

O 

oc 

£20 


10 


-   6-CARTRAIN.-4  MOTOR  CARS,-'1 54  TONS. 
AVQ.  BRAKING  RATE1.75  MILES  PER  HR.  PER  SEC 
STATION  STOP-14 SECONDS. 


012345678 
TIME  IN  SERIES  POSITION,  SECONDS. 

Fig.  56. 

tests  on  a  6-car  train  of  the  Manhattan  Elevated  System 
made  by  H.  S.  Putnam  are  embodied  in  the  curves  of 
Figs.  54,  55  and  56,  which  show  for  a  given  schedule 
speed  the  influence  on  the  percentage  of  coasting  and  per- 
centage saving  in  electrical  energy,  of  acceleration  and 
braking  rates,  and  of  running  time  in  series  position. 

The  motor  performance  curves  and  the  speed  and  power 
curves  derived  from  them  refer  to  a  definite  and  constant 
trolley  voltage.  In  practice  this  voltage  has  not  the  same 
value  at  different  points  on  the  roadway,  owing  to  the  drop 


130  TRACTION  AND   TRANSMISSION. 

of  potential  along  the  trolleys,  on  third  rail,  and  on  feeders 
from  the  substations.  The  minimum  voltage  at  the  car 
should  not  be  less  than  350  volts  for  the  usual  600- volt 
equipment.  Consequently  in  selecting  the  car  equipment 
for  a  proposed  railway  service  due  attention  must  be  given 
to  the  voltage  regulation  on  various  parts  of  the  road. 

Speed  curves  of  cars  operating  on  road  sections  on  which 
the  voltage  is  lower  than  normal  must  be  based  upon  the 
average  voltage  existing  at  the  definite  locality.  With 
series  motors  the  speed  at  constant  load  varies  almost 
directly  with  the  impressed  voltage,  and  hence  the  speed 
of  the  car  at  the  instant  full  line  voltage  is  applied  to  the 
motors  is  lower  when  the  line  voltage  is  below  normal. 
Thus  to  maintain  the  same  services  under  reduced  voltage 
requires  that  the  motor  receive  power  for  a  longer  time, 
and  this  frequently  implies  a  greater  power  consumption. 
Sufficient  trolley  voltage  all  along  the  car  route  is  impor- 
tant, particularly  so  on  grades. 

46.  Gear  Ratio.  —  When  a  railway  motor  takes  a  cer- 
tain current  at  constant  voltage  a  definite  torque  is  devel- 
oped, and  the  corresponding  tractive  effort  produced  by 
the  motor  at  the  base  of  the  car  wheels  depends  entirely 
upon  the  gear  ratio,  that  is,  the  ratio  of  the  number  of 
gear  teeth  to  motor-pinion  teeth.  The  resulting  speed  of 
the  car  for  this  motor  current  is  inversely  proportional  to 
the  tractive  effort,  and  consequently  the  smaller  the  gear 
ratio  the  higher  will  be  the  speed  of  the  car  and  the  lower 
will  be  the  tractive  effort  available  for  acceleration.  There- 
fore, to  maintain  a  specified  initial  rate  of  acceleration 
requires  a  larger  current  through  the  motors  when  geared 
for  high  car  speed  than  when  provided  with  a  large  gear 
ratio  (i.e.,  low  car  speed).  On  the  other  hand,  the  time 


ENERGY   CONSUMPTION. 


that  power  is  on  the  motors  of  a  car  when  operating  over 
a  given  run  is  longer  with  high  gear  ratios  than  with  low 
ratios.  The  effect  of  change  in  gear  ratio  on  the  rate  of 
acceleration  with  a  definite  accelerating  current  and  on 
the  magnitude  of  this  current  with  a  definite  acceleration 
rate,  is  indicated  respectively  in  the  two  following  tables 
which  refer  to  the  24-32-ton  car  equipped  with  four  5o-horse- 
power,  6oo-volt,  direct-current  motors  whose  characteris- 
tic curves  are  shown  in  Fig.  23  for  a  gear  ratio  of  17  to  69 
(or  4.06). 


Gear  ratio. 

Rate  of 
acceleration. 

1-5 

0.48 

2.0 

0.68 

3-o 

i.  08 

4.06 

i-So 

5-o 

1.87 

Gear  ratio. 

Accelerating 
current  per 
motor. 

I-  5 

142 

2.0 

1  10 

3-o 

80 

4.06 

64 

5-o 

55 

(Accelerating  current  • 
=  64  amperes  per  motor.) 


(Acceleration  rate  =  1.5  miles 
per  hour  per  second.) 


By  constructing  speed  and  power  curves  over  a  typical 
run  for  a  given  equipment  when  supplied  with  different 
gears,  and  subsequently  plotting  curves  of  power  consump- 
tion and  of  effective  heating  current  in  terms  of  gear  ratio, 
that  gear  ratio  for  the  equipment  can  be  determined 
which  is  conducive  to  a  minimum  expenditure  of  energy 
and  least  heating  of  the  motors.  In  general,  it  develops 
that  the  most  suitable  gear  ratio  for  motors  of  proper 
capacity  for  a  specified  service  is  that  which  will  yield  the 
lowest  car  speed  consistent  with  the  prescribed  schedule 
speed,  due  allowance  being  made  for  delays.  A  gear  ratio 
so  chosen  will  result  in  a  low  energy  consumption  by  the 
motors  and  a  small  temperature  elevation. 


132  TRACTION  AND   TRANSMISSION. 

PROBLEMS. 

24.  Upon  the  speed  curve  of  Problems  17  and  18  plot  the  curve  of  current 
and  power  input  per  motor  car.     In  determining  the  speed  of  the  car  at 
which  the  transition  from  the  series  to  the  parallel  connection  of  the  motors 
is  made  neglect  the  motor  voltage  drop.     Compute  the  average  current  and 
power  input  per  motor  car  over  the  time  of  the  complete  run. 

25.  Calculate  the  energy  consumption,  in  kilowatt-hours  per  train-mile 
and  in  watt-hours  per  ton-mile,  of  the  train  considered  in  Problems  17,  18, 
and  24. 

26.  How  much  energy  in  kilowatt-hours  is  consumed  by  the  equipment 
of  the  2o-ton  car  mentioned  in  Problems  14  and  15  over  the  run  for  which 
the  service  conditions  are  there  specified?     What  is  the  equivalent  heating 
current  on  this  particular  run? 

27.  Determine  from  the  curves  of  Fig.  51  the  energy  consumption  in 
watt-hours  per  ton-mile  of  the  5o-ton  car  equipped  with  four  75-horsepower, 
single-phase  motors.     Add  8  %  of  the  power  taken  by  the  motors  to  allow 
for  other  losses  in  the  car  equipment. 

28.  Plot  curves  of  initial  current,  full  voltage  speed  with  initial  accelerat- 
ing current,  and  time  of  running  on  reduced  voltage,  all  in  terms  of  the 
rate  of  acceleration,  for  a  loo-ton  New  Haven  electric  locomotive  equipped 
with  four  25o-horsepower,  single-phase  motors  whose  characteristic  curves 
are  shown  in  Fig.  25.     Assume  train  resistance  uniform  at  a  value  of  15 
pounds  per  ton. 

29.  Construct  a  curve  showing  the  maximum  schedule  speed  possible, 
in  terms  of  the  duration  of  a  stop,  for  the  car  whose  typical  speed  curve  on 
a  level  track  is  shown  in  Fig.  31. 

30.  A  motor  car,  weighing  43  tons,  equipped  with  two  2oo-horsepower 
motors  (gear  ratio  20  : 63),  whose  characteristic  curves  are  shown  in  Fig.  24, 
gains  velocity  at  the  rate  of  2  miles  per  hour  every  second  on  a  tangent  level 
track.     Assuming  train  resistance  as  15  pounds  per  ton,  plot  a  curve  of 
the  accelerating  current  required  per  motor  when  the  equipment  is  pro- 
vided with  different  gear  ratios,  in  terms  of  gear  ratio. 


THE  DISTRIBUTING   SYSTEM.  133 


CHAPTER  VII. 
THE  DISTRIBUTING   SYSTEM. 

47.  Classification  of  Conductors.  —  It  is  common  to 
divide  the  conductors  of  the  distributing  system  into  two 
parts,  the  ones  which  convey  current  from  the  station  to 
the  cars  being  termed  positive  and  those  which  return  it 
being  termed  negative. 

The  positive  conductors  may  be  divided  into  three  classes 
as  follows:  (i)  bare  contact  conductors,  such  as  trolley 
wires,  third  rails,  and  T  conductors  in  slot  systems,  from 
which  the  current  for  propulsion  is  taken  by  means  of 
collecting  devices;  (2)  supplementary  conductors,  which  are 
parallel  to  the  contact  conductors,  are  connected  with  them 
at  frequent  or  infrequent  intervals,  and  which  are  designed 
to  increase  or  supplement  their  conductivity;  and  (3)  feeders 
which  extend  from  the  station  to  a  feeding  point  on  the 
contact  or  supplementary  conductors,  and  which  supply 
current  to  them. 

The  negative  conductors  may  be  similarly  classified, 
although  the  bare  conductor  which  receives  current  from 
the  car  is  not  usually  termed  a  contact  conductor.  It 
usually  consists  of  the  connected  track  rails,  although  it 
may  be  a  second  trolley  wire  or  T  conductor  in  a  slot 
system.  Negative  feeders  and  supplementary  conductors 
are  also  common. 

The  contact  conductors  are  usually  divided  into  successive 
sections  each  one  of  which  is  insulated  from  adjacent  sec- 


134  TRACTION  AND  TRANSMISSION. 

tions.     Their  lengths  vary  from  a  few  hundred  feet  to  sev- 
eral miles. 

48.   Contact  Conductors.  —  To  determine  the  drop  as- 
sume a  contact  conductor  BD,  Fig.  57,  fed  at  B  with  / 


Fig.  57- 

amperes,  I\  and  /2  amperes  being  drained  from  it  at  dis- 
tances from  B  of  h  and  /2  feet  respectively.  If  the  specific 
resistance  of  the  conductor  be  p  ohms  per  mil-foot  and  its 
cross  section  be  A  circular  mils,  then  the  drop  from  B  to 
D  is 


or 

e  =  ^  (Wi  +  /2/2)  volts. 
A 

Similarly  in  general,  if  any  number,  n,  of  currents  of  dif- 
ferent magnitudes  Im  be  drained  off  at  different  distances,  lm 
from  B,  the  total  drop  from  B  to  the  most  distant  point  of 
drainage  may  be  expressed  as 


Im)  =   -^  IQ!    VOltS,  (l) 

where  IQ  =  ^™x™y    is  such  a  distance  from  B  that  if  the 
total  current  /  were  carried  that  far  the  resultant  drop 


THE  DISTRIBUTING  SYSTEM  135 

would  be  e  volts.  The  relations  which  exist  between  the 
currents,  the  distances,  and  IQ  are  so  similar  to  those  which 
exist  between  the  elementary  and  total  masses  of  a  body, 
the  respective  distances  of  the  former  from  a  plane,  and  the 
distance  of  the  center  of  gravity  from  the  plane,  that  the 
point  which  is  /0  feet  from  A  is  termed  the  center  of  gravity 
of  the  combined  drainage  load. 

The  total  drop  in  a  section  of  contact  conductor  is  almost 
always  assumed.  Taken  together  with  the  drop  in  the 
negative  part  of  the  system  it  must  not  be  so  great  as  to 
hinder  the  proper  starting  and  operation  of  the  motors  and 
the  proper  functioning  of  the  lamps.  The  maximum  drop 
in  the  negative  conductors  is  usually  made  small  with  a 
view  to  meeting  municipal  ordinances  or  to  preventing 
electrolytic  corrosion.  In  England  it  is  limited  to  seven 
volts.  The  total  drop  varies  from  10  %  to  50  %  of  the  nor- 
mal voltage,  the  smaller  value  ruling  in  all  alternating-cur- 
rent and  in  urban  direct-current  systems,  while  the  larger 
is  found  in  direct-current  interurban  systems.  Knowing, 
therefore,  the  value  of  e,  if  the  length  of  conductor  and  the 
distribution  of  the  load  be  given,  the  proper  cross  section 
may  be  determined  from  (i)  as 

A  =  -10I  circular  mils.  (2) 

e 

The  minimum  cross  section  of  the  contact  conductor  is 
dictated  by  mechanical  considerations  in  the  case  of  trolley 
wires,  and  by  manufacturing  standards  in  the  case  of  third 
rails.  The  size  of  trolley  wires  is  usually  Nos.  ooo  or  oooo 
B.  &.  S.,  although  No.  o  has  been  used.  With  double- 
track  roads  and  those  single-track  roads  which  employ 
twin  trolley  wires  the  sum  of  the  cross  sections  of  the  two 
wires  should  be  taken.  If,  therefore,  the  cross  section,  the 


i36 


TRACTION  AND   TRANSMISSION. 


drop,  and  the  load  distribution  be  known,  the  limiting 
length  of  contact  conductor  which  can  be  fed  from  a  single 
feeding  point  may  be  determined  by  means  of  formula  (i). 
The  specific  resistance  of  third  rails  varies  with  their 
chemical  composition.  Armstrong  recommends  the  follow- 
ing limitations  as  to  ingredients: 

Carbon  not  to  exceed 0.12  per  cent 

Manganese  not  to  exceed 0.40     ' 

Sulphur  not  to  exceed 0.05     "      " 

Phosphorus  not  to  exceed o.io     ' 

Such  compositions  result  in  a  resistivity  of  approximately 
14  microhms  per  centimeter  cube  at  20°  C.,  a  value  which 
is  seven  and  three-quarters  that  of  commercial  copper.  The 
following  table  of  rail  resistances  is  based  upon  this  value: 

RESISTANCE  OF  THIRD   RAILS   INCLUDING  BONDS 


Rail  weight  in  pounds 
per  yard. 

Resistance  in  ohms 
per  mile. 

40 

0.093 

SO 
60 

0.074 
0.062 

70 
80 

0-053 
0.046 

90 
100 

0.042 
0.038 

110 

0.034 

Inasmuch  as  the  current  taken  by  a  car  varies  with  the 
time  and  location  of  the  car  and,  in  congested  districts,  is 
subject  to  further  variations  due  to  traffic  conditions  and 
the  idiosyncrasies  of  the  motorman,  it  is  customary  to 
assume  a  uniform  drainage  of  70  amperes  per  foot  from 
the  contact  conductor  when  treating  urban  or  suburban 
problems  where  several  cars  are  taking  current  at  the  same 
time  from  the  same  section.  The  value  of  70  changes 


THE   DISTRIBUTING    SYSTEM. 


137 


during  the  day,  and  for  calculating  limiting  conditions 
the  rush-hour  value  should  be  taken.  Its  average  value 
may  be  determined  by  multiplying  the  average  current 
taken  by  each  car  in  passing  over  the  section  by  the  num- 
ber of  cars  on  the  section  at  one  time  and  dividing  this 
product  by  the  length  of  the  section.  The  ratio  of  its 


3.0 


2.5 


I  MAX. 


2.0 


1.5 


1.0 


10 


20  60 

NUMBER  OF  CARS. 

Fig.  58. 


40 


50 


maximum  to  its  average  value  may  be  determined  by 
reference  to  Fig.  58,  which  is  based  upon  experience. 

End  Feeding.  Consider  a  section  of  length  L  feet,  fed 
at  one  end  as  in  Fig.  57,  and  let  it  be  uniformly  loaded. 
Since  the  current  density  70  =  I/L,  and  the  distance  of  the 
center  of  gravity  of  the  aggregate  load  /0  =  L/2,  the  total 
drop  over  the  section  is 


e=^/  =  iT/()VOlts' 


whence 


L  = 


P/o 


feet. 


(3) 


(4) 


138  TRACTION  AND   TRANSMISSION. 

The  total  drop  is  therefore  proportional  to  the  square  of 
the  length  of  the  section,  and  the  maximum  permissible 
length  of  section  is  to  be  obtained  by  use  of  equation  (4) . 

Center  Feeding.  If  the  section  be  fed  at  its  middle  point 
instead  of  at  the  end,  the  permissible  length  of  contact 
conductor  section  is  twice  that  indicated  by  equation  (4). 
Such  a  system  is  schematically  represented  in  Fig.  59,  and 
is  considered  ideal  from  an  operating  viewpoint,  for  each 
section  may  be  controlled  by  a  circuit  breaker  at  the  station 
in  the  feeder  supplying  that  section.  This  gives  complete 

BREAKERS          F£EDERS 


SECTIONAL  CONTACT  CONDUCTORS 


TRACK 


Fig.  59- 

control  of  each  and  every  section  in  case  of  overload,  short 
circuit,  accident,  or  repairment.  It  is  the  system  most 
frequently  used  for  urban  roads.  It  may  be  desirable  to 
connect  the  adjacent  ends  of  the  sections  of  the  contact 
conductor  through  a  section  breaker  which  may  be  located 
on  a  near-by  pole.  When  these  circuit  breakers  are  closed 
there  results  an  equalization  of  the  current  distribution  and 
the  conductivity  of  the  whole  positive  system  becomes 
available.  The  remoteness  of  these  breakers  from  the 
station,  however,  is  objectionable  as  lacking  accessibility. 
Watts  Lost  in  Conductor.  While  the  cross  section  of  the 
contact  conductor  is  usually  prescribed  by  the  maximum 
permissible  drop  or  by  mechanical  considerations,  cases 
may  arise  where  a  larger  cross  section  will  prove  more 


THE   DISTRIBUTING   SYSTEM.  139 

economical.     In  such  cases  the  power  lost  in  the  contact 
conductor  may  be  found  as  follows  : 
Let  Ie  =  effective  current  per  foot  in  amperes, 
R  —  resistance  per  foot  in  ohms, 
L  =  total  length  of  conductor  from  feeding  point  in 
feet. 

Then  the  power  lost  in  an  elementary  length  dl  of  the 
conductor  at  a  distance  /  feet  from  the  feeding  point  is 

dP  =  [I^(L  -  /)]2  Rdl 
and  the  total  power  lost  is 


or 

P  =  -Ie2R  watts.  (5) 

o 

For  a  section  fed  at  one  end,  L  represents  the  length  of  the 
section.  If  the  section  be  fed  at  the  middle  and  be  2  Z,  feet 
long,  the  loss  will  be  twice  that  given  by  equation  (5). 
The  proper  cross  section  is  then  determined  by  Kelvin's 
law  as  in  §62. 


FEEDING 
POINT 


Fig.  60. 


D 


49.  Branches.  —  When  a  contact  conductor  section  is 
bifurcated  because  of  a  branch  in  the  roadway  as  shown 
in  Fig.  60,  and  when  it  is  fed  at  the  point  of  bifurcation,  the 
drainage  current  on  each  part  may  be  found  as  follows: 


140  TRACTION   AND   TRANSMISSION. 

Let  m  =  number  of  cars  operating  between  A  and  B, 

n  =  number  of  cars  operating  between  A  and  D. 
Then  at  any  time: 

number  of  cars  between  A  and  C  =  n\  =  m     ]     +  n  - — ~ 

fri  +  ^2         n  T 


number  of  cars  between  C  and  B  =  n2  =  m  - — —  > 
.  li-rh 

and 

number  of  cars  between  C  and  D  =  nz  =  n      8     • 

H  ~r  ^3 

The  drainage  current  per  unit  length,  J^,  for  any  part  of 
the  section  may  be  expressed  in  terms  of  the  average  current 
per  car,  Ic,  as 

Ion  =  —y—2  amperes. 

50.  Collecting  Devices.  —  The  conduction  of  current 
to  the  motors  on  the  cars  from  the  contact  conductor  is 
accomplished  by  means  of  wheels,  rollers,  or  sliding  bows 
for  trolley  wires,  of  shoes  for  third  rails,  and  of  plows  for 
slot  systems. 

Trolley  wheels  are  grooved  wheels  of  from  3.5  to  6  inches 
in  diameter  and  are  mounted  in  self-lubricating  bearings 
at  the  end  of  a  trolley  pole.  The  other  end  of  the  pole 
is  movably  mounted  in  a  trolley  table  upon  the  top  of  the 
car  and  is  controlled  in  a  vertical  plane  by  springs  and  levers 
so  as  to  exert  a  fairly  uniform  pressure  between  the  wheel 
and  the  trolley  wire,  irrespective  of  the  angle  of  elevation 
of  the  pole.  This  pressure  varies  from  15  to  40  pounds. 
The  maximum  current  which  can  be  collected  by  this 
means  decreases  with  the  speed  and  is  represented  in  the 
curve  of  Fig.  61.  If  it  be  necessary  to  collect  more  current 
than  that  indicated  by  this  curve,  either  a  plurality  of 


THE  DISTRIBUTING   SYSTEM. 


141 


trolley  wheels  or  some  other  form  of  collecting  device  must 
be  used.  When  the  direction  of  car  movement  is  reversed, 
it  is  necessary  to  turn  the  trolley  pole  through  180°  in  a 
horizontal  plane  so  that  it  may  incline  to  the  rear  of  the 
car.  To  avoid  this  shifting,  use  is  sometimes  made  of 
cylindrical  rollers  mounted  in  pantograph  frames  on  top  of 


1000 

.800 
$ 
£  600 

CL 

2 

<400 

200 


10  20  30  40 

MILES  PER  HOUR. 

Fig.  61. 


50 


60 


the  cars.  The  contact  is  not  as  good  as  in  the  case  of  a 
grooved  wheel,  and  the  inertia  of  the  heavy  frame  tends  to 
produce  arcing  at  the  contact  with  high  speeds. 

The  sliding-bow  collector,  mounted  upon  a  spring-con- 
trolled pole  or  pantograph  frame,  is  rapidly  coming  into  use, 
especially  in  connection  with  alternating-current  systems. 
This  form  of  collector  is  more  common  in  Europe  than  in 
this  country. 

The  construction  and  principle  of  operation  of  shoes 
depend  upon  the  character  of  the  third-rail  mounting 
with  which  they  are  to  be  used.  With  an  overrunning 
third  rail,  as  used  on  the  Manhattan  Elevated  Railroad  in 
New  York,  and  mounted  as  shown  in  Fig.  62,  the  pressure 
between  the  shoe  and  the  rail  surface  is  due  to  the  weight 


142 


TRACTION   AND   TRANSMISSION. 


of  the  shoe.  The  construction  of  a  shoe  adapted  to  such 
conditions  is  shown  in  the  figure.  In  case  the  third  rail 
is  protected  against  sleet  and  ac- 
cidental contact  by  an  insulating 
barrier  at  one  side  and  over  its 
top,  or  is  of  the  underrunning  type, 
the  shoe  is  generally  hinged  and 
the  contact  pressure  is  controlled 
by  springs.  The  construction  of 
such  a  shoe  for  use  with  the  latter 
type  of  third  rail  is  shown  in 
Fig.  63.  The  current-collecting 
capacity  of  shoes  is  very  large, 
2000  amperes  per  shoe  for  speeds 
UP  to  35  miles  per  hour  being 
attainable. 

Since  the  plows  used  with  slot 
systems  must  conduct  current  to 
and  from  the  car  motors,  their 
circuits  must  be  carefully  insu- 
lated from  each  other,  and,  as  the 
slot  aperture  is  of  necessity  nar- 
row, they  usually  assume  a  thin, 
flat  form.  Spring-controlled 
wings  at  their  lower  ends  serve 
to  form  the  circuit  with  the  con- 
tact conductors  on  either  side  in 
the  conduit  underneath  the  slot. 

51.  Supplementary  Conductors. 
—  When    a   supplementary   con- 
ductor is  of  uniform  cross  section  throughout  its  length 
and  is  connected  with  the  contact  conductor  at  successive 


THE   DISTRIBUTING   SYSTEM.  143 

points  near  to  each  other,  the  two  may  be  considered  as 
a  single  composite  contact  conductor  of  cross  section  equal 
to  the  sum  of  the  two. 

The  economic  use  of  copper  requires,  however,  that  the 
cross  section  of  the  supplementary  conductor  be  not  uni- 


Center  L/ne  Tft/rtf/fo/'/ 
I 


Fig.  63. 

form.  Consider  such  a  composite  contact  conductor  sec- 
tion to  be  fed  with  /  amperes  at  one  end  and  to  be  divided 
into  m  short  elements,  each  of  length  /  feet,  and  of  different 
cross  sections,  that  of  the  nth  element  from  the  remote  end 
being  yn  circular  mils.  For  a  uniform  drain  of  current  IQ 


144  TRACTION  AND   TRANSMISSION. 

amperes  per  foot,  the  current  in  the  nth  element  is  nl^, 
the  volume  of  the  element  is  ynl  circular  mil-feet,  its  resist- 
ance is  pl/yn  ohms,  and  the  drop  over  it  is  nplj?/yn  volts. 
If  v  be  the  total  volume  of  copper  and  e  be  the  total  drop, 
then 

m  m 

v  =^lyn  =  l^yn  circular  mil-feet       (i) 
and 


e  = 


volts.  (2) 


Therefore  substituting  the  value  of  /  from  (2)  in  (i), 


/ —     ^  '" 
V/  —  — l  circular  mil-feet.     (3) 

•       _  T  i    m. 

P*  o 


In  order  that  the  copper  volume  v  may  be  a  minimum 
must  be  a  minimum,  which  involves  the  conditions  that 


m  m 


V  yn  be  a  minimum  while  ^\n/ynj  or  the  total  drop,  remain 

constant.  If  each  term  of  the  latter  be  multiplied  by  an 
unknown  constant  C,  to  be  determined  later,  the  result 
will  still  be  a  constant.  Further,  if  each  term  of  the  result 

m 

be  added  to  the  corresponding  term  of  the  series  V%,  a 


new  series  will  be  formed,  of  the  form  z  =  V( 

i*\y» 

which  also  must  be  a  minimum.    Therefore 


THE   DISTRIBUTING   SYSTEM.  145 

and  since  nl  =  x,  the  distance  in  feet  of  any  chosen  point 
from  the  remote  end,  substituting  the  value  of  n 

l~Cx 
yx  =  y  — -    circular  mils.  (4) 

To  determine  the  value  of  C,  consider  that  the  drop  in  an 
element  of  length  dx  at  a  distance  x  from  the  remote  end  is 

,        ploxdx         T      1 1     /-  , 
de  =  -        -  =  PIo\/-Vxdx', 
yx  V  C 

therefore  the  total  voltage  drop  is 

e  =  P/O  \/| £**<**  =  P*o  Y/l  -  L1  volts.  (5) 

Since  the  total  entering  current,  /,  is  equal  to  the  product 
of  70  and  the  total  length  of  the  section,  L,  the  value  of 


—  from  equation  (5)  becomes 

/C  _2plVl. 

V  /      3     ^ 
consequently 


yx  =  —^—     -  Vie  circular  mils.  (6) 

3  e 

This  equation  shows  that  the  curve  which  relates  total 
cross  section  of  supplementary  and  contact  conductor  with 
distance  from  the  remote  end  is  a  parabola  with  its  vertex 
at  the  remote  end.  Of  course  it  is  not  practicable  to  con- 
struct a  conductor  with  such  a  varying  cross  section,  but 
it  is  common  to  reduce  the  cross  section  by  steps  as  the 
remote  end  is  approached. 

The  connection  of  the  supplementary  to  the  contact  con- 
ductor at  many  points  involves  considerable  expense  espe- 
cially when  made  through  contact  switches.  It  is  therefore 


146 


TRACTION   AND    TRANSMISSION. 


common  practice  to  employ  a  moderate  number  of  connec- 
tions and  to  feed  sections  at  each  end  and  often  from 
separate  substations.  In  many  instances  this  arrangement 
is  used  when  the  load  is  concentrated  rather  than  uniformly 
distributed.  In  such  cases  the  determination  of  the  proper 


Fig.  64. 

disposition  of  copper  is  involved  and  is  best  arrived  at  by 
trials  based  upon  assumed  distributions  of  copper  and  of 
load. 

Assume  a  system  connected  as  in  Fig.  64  which  is  elec- 
trically equivalent  to   the  arrangement  shown  in  Fig.  65, 


Fig.  65. 

where  the  resistances  of  the  various  branches  and  the 
voltage  at  the  substations  are  known  and  the  equivalent 
resistances  R  of  the  load  and  x  of  the  rest  of  the  conducting 
system,  out  and  back  from  both  substations  and  considered 
as  connected  in  parallel,  are  to  be  found.  The  problem  is 
solved  by  applying  Kirchhoff's  laws,  which  result  in  the 
following  equations,  where  the  resistances 


THE  DISTRIBUTING   SYSTEM. 


A  =  a  +  b  +  c 
B=d+f+g 
C  =  b  +  d  +  h 


ohms. 


AIi.  -6/3    +  IR    =    E 

BI2     -dlz    -IR    =-E 

-6/1  -  d!2    +C/3  =     o 

/I      ~/2  =        / 

Solving  for  R  by  means  of  determinants 


(7) 


(8) 


R  = 


A 

0 

-b 

I 

0 

B 

-d 
—  i 

-b 
-d 
C 
o 

E 
-  E 

0 

/ 

A 
B 

-b 
-d 

M)C 

(E-AT)/I 

-E/I 
b 

A 

0 

-b 

i 

0 

B 

-d 
—  i 

-b 
-d 
C 

0 

/ 

-/ 
o 
o 

A 

-  b 
i 

B      -(b+d) 
-d          c 

—  I                0 

ohms.  (9) 


RI  = 


volts.  (10) 


Whence  the  voltage  impressed  upon  the  load  is 

E(b+d)2-E(A+B)C-(Ad2+Bb2-ABC)I. 

(b  +  d)*  -  (A  +  B)C 
The  drop  e  between  either  substation  and  the  load  is 

e  =  xl  =  E  -  RI  volts,  (n) 

where  x  is  the  equivalent  resistance  in  ohms  of  the  con- 
ducting system  between  the  substations  and  the  load.  The 
drop  between  a  substation  and  any  point  with  a  plurality 
of  variously  located  loads  is  equal  to  the  sum  of  the  drops 
produced  by  each  load. 

52.  Graphic  Time-table.  —  Since  the  reason  for  the 
employment  of  supplementary  conductors  is  the  preven- 
tion of  an  excessive  drop  of  voltage  between  the  substa- 
tions and  the  cars,  the  conductors  must  be  of  adequate 


148  TRACTION  AND   TRANSMISSION. 

cross  section  to  cope  with  the  worst  condition  likely  to 
arise  in  the  operation  of  the  electric  railway.  As  the 
voltage  drop  varies  with  the  current  and  with  the  resist- 
ance, and  the  latter  is  proportional  to  the  length  of  the 
conductors,  the  worst  condition  will  be  when  a  maximum 
total  current  is  taken  by  cars  at  a  maximum  distance  from 
both  substations.  To  determine  this  condition  use  is 
made  of  graphic  time-tables  or  train-sheets  for  the  proposed 
service;  such  a  curve  is  shown  in  Fig.  66.  It  consists  of  a 
set  of  intersecting  curves,  each  one  constituting  the  locus 
of  the  correlated  time  and  place  relations  of  a  car  or  train. 
The  ordinates  may  represent  the  hours  of  the  day,  while 
the  abscissae  represent  distances  from  the  road  terminus 
in  miles.  The  curves  are  usually  considered  as  made  up 
of  straight-line  elements  either  inclined  or  perpendicular  to 
the  axis  of  abscissae.  The  cotangent  of  the  angle  between 
a  portion  of  the  curve  and  a  parallel  to  the  axis  of  abscissae 
represents  the  corresponding  speed  in  miles  per  hour.  If 
the  elements  be  straight  the  speed  is  constant,  and  in 
plotting  these  curves  the  average  running  speed  is  assumed 
to  be  maintained  throughout.  The  perpendicular  elements 
represent  stops  of  durations  proportional  to  the  lengths  of 
the  elements.  The  ordinate  of  a  point  where  two  curves 
cross  each  other  gives  the  time  when  the  corresponding 
cars  meet  each  other,  while  its  abscissa  determines  the  neces- 
sary location  of  a  turnout,  if  the  road  have  but  a  single 
track.  For  a  specific  problem  the  time-table  should  have 
indicated  upon  it  also  the  distribution  of  copper  and  the 
location  of  towns,  villages,  and  substations. 

Confining  the  attention  to  a  single  section  of  the  road, 
and  assuming  an  average  value  of  current  taken  by  a  car 
when  running  and  another  greater  value  when  starting,  the 


THE   DISTRIBUTING  SYSTEM. 


149 


§ 


A 


A 


i 

§-H 


v 


150  TRACTION  AND  TRANSMISSION. 

magnitudes  of  the  currents  and  the  distances  from  the  sub- 
stations of  their  points  of  drainage,  corresponding  to  any 
chosen  time,  can  be  readily  obtained.  A  comparison  of  the 
results  for  different  times  readily  reveals  the  worst  condi- 
tion likely  to  arise.  With  single-track  interurban  roads 
giving  infrequent  train  service  such  condition  is  likely  to 
occur  when  and  where  two  trains  pass  each  other. 

Having  determined  the  werst  condition,  the  adequacy  of 
the  assumed  distribution  of  copper  can  be  determined  by 
the  method  outlined  in  the  preceding  section.  The  mini- 
mum voltage  permissible  at  the  car  on  6oo-volt  systems  is 
300  volts,  or  with  high-class  service  350  volts. 

In  the  case  of  a  supplementary  conductor  with  numerous 
connections  with  a  contact  conductor  which  extends  between 


0 


i    i    i    i    i    i 


i    i    i    i    i    i    i    i    i    i    i    i 


Fig.  67. 

two  substations  and  is  fed  by  both,  the  drop  produced  by 
a  concentrated  load  is  proportional  to  the  current  and  to 
the  distance  from  the  nearer  substation.  Consider  the 
conditions  as  represented  in  Fig.  67.  If  R  be  the  resistance 
in  ohms  per  foot  of  combined  conductor,  the  drop  is 

e  =  Rhli  =  Rh(L  -  /O  volts.  (i) 

But  /  =  1 1  +  /2  amperes;  (2) 

hence  e  =  RI  (i  -  jj  h  volts.  (3) 

Therefore,  for  a  given  current  /,  the  drop  increases  with 
increase  of  h  from  h  =  o  to  h  =  —  -  These  equations  also 

O 


THE  DISTRIBUTING  SYSTEM.  151 

show  that  the  portions  of  the  current  supplied  to  a  car  by 
the  two  substations  vary  inversely  as  their  respective  dis- 
tances from  the  car. 

53.  Feeders.  —  Although  supplementary  conductors  are 
often  termed  ''auxiliary  feeders"  or  simply  "feeders,"  the 
latter  term  is  used  in  this  text  to  represent  conductors 
which  extend  from  the  station  to  a  single  feeding  point 
and  which  carry  the  same  current  at  the  same  time 
through  every,  cross  section.  The  cross  section  of  a  feeder 
is  often  determined  from  economical  considerations  and  by 
the  use  of  Kelvin's  law  as  modified  by  Kapp:  The  most 
economical  area  is  that  for  which  the  annual  cost  of  energy 
wasted  is  equal  to  the  annual  interest  on  that  portion  of 
the  capital  outlay  which  can  be  considered  proportional  to 
the  weight  of  metal  used. 

Let  I  =  maximum  current  in  amperes  carried  by  the 

feeder, 

L  =  length  of  feeder  in  feet, 
A  =  its  cross-section  in  circular  mils, 
h  =  effective  annual  hours  of  operation  at  maximum 

current, 

p  --=  resistance  of  feeder  in  ohms  per  mil-foot,  and 
w  =  weight  of  a  mil-foot  in  pounds. 

Then  the  resistance  of  the  feeder  is  ^—  ohms,  and,  if  the 

A 

cost  per  kilowatt-hour  delivered  to  the  feeder  be  cz  dollars, 
the  annual  expense  for  energy  lost  in  the  feeder  is 

dollars.  .   (i) 

At  a  cost  of  c2  dollars  per  pound  of  feeder  conductor  and 


152  TRACTION  AND  TRANSMISSION. 

at  a  rate  for  interest  and  depreciation  of  p2)  the  annual 
charge  against  capital  outlay  for  feeder  conductor  is 

Cf"  =  p2c2wLA  dollars.  (2) 

With  overhead  construction  the  cost  of  insulators  and  of 
installing  the  feeder  will  be  independent  of  the  cross-section 
for  a  specific  case.  Therefore  the  most  economic  cross- 
section  is  that  which  will  make  C/  +  Cf"  a  minimum,  in 
which  case  C/  =  C/'  and  the  economic  cross-section  is 


A  =  /  v/ -  -  circular  mils.  (3) 

Hence  the  maximum  economic  drop  is 


The  reciprocal  of  the  radical  in  equation  (3)  may  be  termed 
the  economic  current  density.  Often  the  maintenance  of 
a  suitable  operating  voltage  or  the  inevitable  heating  of  a 
feeder  precludes  the  use  of  the  economic  cross  section.  Long 
feeders  may  be  fed  from  a  special  bus  at  the  station  at  a 
potential  somewhat  in  excess  of  the  normal  station  voltage. 

In  case  the  feeders  are  to  be  placed  underground,  an 
expression  must  be  obtained  for  the  annual  expense  charge- 
able against  the  cost  or  rental  of  conduit  ducts  in  terms 
of  the  feeder  cross-section.  This  expression  must  then  be 
added  to  equations  (i)  and  (2)  before  differentiating  in  order 
to  obtain  a  minimum. 

Boosters.  —  In  the  case  of  feeding  points  remote  from  the 
station  the  cross  section  of  feeders  as  prescribed  by  the 
permissible  drop  may  be  very  large  and  may  entail  an  almost 
prohibitive  first  cost.  The  cross  section  may  be  materi- 
ally reduced  if  a  booster  be  inserted  in  the  feeder  circuit. 


THE   DISTRIBUTING  SYSTEM.  153 

Whether  or  not  a  booster  should  be  used  depends  upon 
its  cost  and  the  expense  of  its  operation  and  maintenance 
as  compared  with  the  saving  resulting  from  the  reduced 
feeder  cross  section.  The  determination  of  the  advisabil- 
ity of  its  use  and  of  its  voltage  may  be  made  as  follows, 
neglecting  the  losses  in  the  booster: 
Let  x  =  maximum  voltage  of  booster, 

ef  =  maximum  total  drop  in  boosted  feeder, 
/  =  maximum  amperes  in  feeder, 
pi=  interest,  depreciation,  etc.,  on  cost  of  booster, 
/  and  g  =  cost  constants. 

Then 

Ix 

Capacity  of  booster  =  -  K.W. 
1000 

Ix 

Cost  of  booster  —f  +  g  -  dollars. 

1000 

Hence  the  annual  interest  and  depreciation  on  the  booster  is 

Ix  \ 
g  -  )  dollars. 

If  h  be  the  yearly  effective  hours  of  feeder  operation  and 
GZ  be  the  cost  in  dollars  of  generating  a  K.W.-hour,  the 
annual  cost  of  energy  lost  in  the  feeder  is 


C2  =  hc3  dollars.  (5) 

IOOO 

If  the  length  of  the  feeder  be  L  feet,  and  its  weight  be 
w  pounds  per  mil-foot,  its  cross  section  is 

A  =  —    -  circular  mils,  (6) 

x  +  e/ 
and  its  weight  is 

TT7      wpIL?  ,  N 

W  =  -    —   pounds.  (7) 


154  TRACTION  AND   TRANSMISSION. 

At  a  cost  of  c2  dollars  per  pound  and  a  rate  of  interest, 
etc.,  of  pz  per  cent,  the  annual  feeder  expense  is 

C3  =  ^^^-2  dollars.  (8) 

x  +  ef 

The  total  annual  feeder  and  booster  expense  therefore  is 

C  =  Ci  +  C2  +  C3, 
or 

dollars.    (  ) 


looo/  1000  x  +  ef 

In  order  that  this  expression  may  be  a  minimum  its  differ- 
ential coefficient  with  respect  to  x  must  equal  zero,  or 

dC  gl     ,    I  he  3      CzptwpIL2 

~j~  =  Pl~  ~  ~  "7  —     —  \«~  =  °» 

dx  1000      1000       (x  +  ef)2 

therefore 

,     .      N2 

and 


r      /IOOO  CipiWp  ,  ,       v 

=LV  "7~  rSr  -^/  voits.  (10) 

£/* 


Since  rx;  must  be  a  positive  quantity,  that  value  of  L  which 
makes  it  equal  to  zero  is  the  minimum  length  of  feeder  with 
which  the  use  of  a  booster  is  advisable.  It  should  be  noted 
that  this  minimum  length  increases  as  the  yearly  hours  of 
boosted-feeder  operation  increase.  Boosters  are  therefore 
to  be  especially  recommended  for  intermittently  operated 
feeders.  If  the  average  efficiency  of  the  booster  set  be  e, 
multiplication  of  the  term  c3h  in  (10)  by  (2  —  e)  will  include 
the  losses  of  the  set. 

With  the  following  values  for  the  constants  —  those  in 
brackets  being  suggestive  of  the  order  of  magnitude  - 
equation  (10)  may  be  simplified  for  use  with  copper  feeders: 


THE  DISTRIBUTING  SYSTEM.                        155 

p  =  10.5.  €3=  [0.006]. 

w  =  0.00000303.  pi=  [o.io]. 

c2=  [0.17].  /  =  [300]. 

#2=    [0.06].  g    ='[28]. 


8  +  0.006 /* 

For  a  total  boosted-feeder  drop  of  50  volts  and  continuous 
operation  of.//  =  24  X  365  =  8760  hours,  the  minimum 
length  of  feeder  to  be  boosted  is  found  by  making  x  =  o. 
It  is 

L  =  20,650  feet. 

An  infrequent  operation  would  indicate  a  poorer  load  factor 
and  accordingly  higher  cost  per  kilowatt-hour  £3.  Assum- 
ing h  =  1000  hours  and  £3  =  o.oi  the  minimum  length 
becomes 

L  =  10,000  feet. 

54.  Track  Rails.  —  The  size  of  track  rails  is  determined 
by  consideration  of  the  mechanical  requirements  of  the 
rolling  stock,  the  schedule  speed,  and  the  character  of 
ballast.  The  common  sizes  weigh  from  60  to  100  pounds 
per  yard  of  length.  The  specific  resistance  varies  with 
the  chemical  constitution  and,  as  carbon  and  manganese 
are  usually  present  to  the  extent  of  about  one-half  per  cent, 
amounts  to  about  20  microhms  per  cubic  centimeter, 
while  that  for  standard  copper  at  o°  C.  is  1.594.  It  is 
convenient  to  assume  that  for  average  temperatures  it  is 
ten  times  that  of  commercial  copper. 

The  usual  length  of  a  rail  is  30  feet,  although  twice  this 
length  is  sometimes  used.  In  order  satisfactorily  to  return 
the  current  to  the  station  from  the  car,  the  rail  sections 
must  be  conductively  connected  with  each  other  by  means 


150  TRACTION  AND  TRANSMISSION. 

of  bonds.  These  bonds  are  often  made  of  copper,  which 
has  a  much  larger  temperature  coefficient  of  expansion 
than  steel.  As  a  consequence,  it  is  not  easy  to  maintain 
a  good  electrical  contact  between  a  copper  bond  terminal 
and  the  rail,  under  varying  temperatures  and  the  displace- 
ments caused  by  traffic.  Many  forms  of  these  bonds  have 
therefore  been  devised.  The  most  satisfactory  forms  have 
their  terminals  either  brazed  to  the  rail  or  mechanically 
expanded  in  a  hole  in  the  web  or  flange  of  the  rail.  When 
heavy  current-carrying  capacity  is  desirable  and  the  den- 
sity of  traffic  warrants  the  expense  the  rail  sections  may  be 
welded  to  each  other. 

It  is  desirable  to  use  a  pair  of  bonds  for  each  joint,  when 
they  are  of  copper,  to  insure  continuity  of  the  circuit  in 
case  one  bond  should  fail.  With  such  bonding  the  resist- 
ance per  mile  of  30-foot  rails  may  be  assumed  as  10  %  larger 
than  if  the  rail  were  continuous. 

For  convenience  in  calculating  the  voltage  drop  in  tracks 
the  following  values  for  the  resistance  of  two  track  rails  in 
parallel  including  that  of  g-inch  bonds  of  half  the  carrying 
capacity  of  the  rail  are  given: 


RESISTANCE  OF  TRACK  RAILS  INCLUDING  BONDS. 


Weight  of  rail, 
pounds  per  yard. 

Resistance  per  mile, 
ohms. 

40 

0.066 

50 
60 
70 
80 

0-053 
0.044 
0.038 
0.033 

90 

0.030 

IOO 

0.027 

no 

0.024 

THE  DISTRIBUTING  SYSTEM.  157 

55.  Negative  Track  Feeders.  —  In  those  systems  which 
make  use  of  the  earthed  track  rails  for  returning  current 
from  the  car  motors  to  the  generating  station,  differences 
of  potential  exist  between  different  points  along  the  rails; 
as  a  consequence,  the  neighboring  soil  takes  a  part  in  the 
conduction  of  the  return  current  owing  to  the  presence  in 
it  of  moisture,  of  dissolved  substances,  and  of  pipes  or  other 
metallic  subsurface  structures.  At  the  points  where  the 
current  leaves  the  last  to  enter  the  connection  from  the 
negative  bus  at  the  station,  electrolytic  corrosion  occurs 
to  an  extent  dependent  upon  the  ampere-hours  conducted. 
It  is  therefore  desirable  that  this  leakage  current  from  the 
rails  should  be  made  as  small  as  possible.  Its  magnitude 
is  dependent  upon  that  of  the  potential  differences  along 
the  rails,  and  varies  inversely  as  the  resistance  offered 
by  the  earth.  It  is  not  often  that  the  engineer  can  alter 
the  earth  resistance,  but  he  can  materially  vary  the  poten- 
tial distributions  along  the  rails  by  using  negative  sup- 
plementary conductors  or  feeders,  connected  to  the  track 
at  predetermined  points,  which  serve  as  auxiliary  return 
conductors.  Owing  to  the  large  cross  section  offered  to 
the  current  by  the  earth,  its  chief  resistance,  outside  of 
that  existing  at  the  ground  plate  for  the  negative  bus  at 
the  station,  is  that  due  to  the  layers  of  soil  in  the  immediate 
vicinity  of  the  rails,  and  this  may  be,  and  hereinafter  is, 
considered  as  a  transition  resistance  of  a  ohms  per  foot 
length  of  track  (two  or  four  rails)  and  varying  inversely  as 
the  length.  In  the  case  of  a  track  whose  rails  are  connected 
to  the  ground  and  to  the  negative  bus  at  the  power  house, 
if  the  excesses  of  potential,  £,  of  the  various  points  in  the 
track  above  that  of  the  negative  bus  be  represented  by  the 
ordinates  of  the  curve  of  Fig.  68,  while  the  abscissae  repre- 


TRACTION  AND   TRANSMISSION. 


sent  distances  in  feet  from  the  power  house,  then  the 
leakage  current  dle,  escaping  at  the  point  /  to  the  soil 
from  an  elementary  length,  dl,  of  track,  is  represented  by 
the  proportionality 


and  the  total  leakage  current  is  proportional  to  the  area 


50 


h-  CD 

UJ  UJ 

m  z 

CO  Q 


0  200  400  600  800  1000 

DISTANCE  FROM  POWER  HOUSE,  I,  IN  FEET. 

Fig.  68. 

included  between   the  potential   curve   and   the   axis   of 
abscissae,  or 

L  (2) 


i  C 
a  Jo 


In  order  to  compare  the  relative  merits  for  the  reduction 
of  leakage  current  of  various  proposed  dispositions  of  the 
same  amount  of  return  copper,  it  is  desirable  that  analyti- 
cal expressions  be  obtained  for  e  in  terms  of  the  distances, 
/,  from  the  power  house  for  each  proposed  disposition. 
Substitution  can  then  be  made  in  (2)  and  that  disposition 
which  yields  the  minimum  value  of  the  integral  may  be 
adopted. 

As  an  illustration,  consider  a  single  generator  supplying 


THE  DISTRIBUTING   SYSTEM.  159 

/  amperes  to  trolley  feeders  for  a  single-track  road  extend- 
ing L  feet  in  only  one  direction  from  a  station,  the  load 
being  uniformly  distributed  along  the  line.  Assume  that  the 
negative  terminal  of  the  generator  is  grounded  at  the  station 
and  that  one  negative  supplementary  conductor  of  uniform 
cross  section,  and  bonded  to  the  rails  at  short  intervals, 
extends  from  the  station  to  the  end  of  the  line. 
Let  /  =  distance  in  feet  of  any  point  on  the  line  from  the 

station, 

i  =  current  at  this  point  in  amperes, 
e  =  voltage  of  track  at  this  point  above  negative 

terminal  of  generator, 
r  =  resistance  in  ohms  per  foot  of  return,  including 

rails  and  negative  supplementary  conductor, 
p  =  ohms  per  mil-foot  of  copper, 
Ai=  copper  cross  section  in  circular  mils  equivalent 

in  conductivity  to  the  track  rails, 
Ac=  cross  section  of  negative  supplementary  conduc- 

tor in  circular  mils. 
Then 

amperes,  (3) 


volts.        (5) 


The  curve  coordinating  voltage  to  distance  is  therefore  a 
parabola,  and  the  area  contained  between  it  and  the  /  axis, 
that  is,  the  value  of  the  integral  in  equation  (2),  is 


C 

\ 

Jo 


L  ji  P1      L2  f*\ 

edl  =  --——-  (6) 


i6o 


TRACTION  AND   TRANSMISSION. 


George  I.  Rhodes  has  compared  various  dispositions  of 
return  copper  and  concludes  that  a  maximum  reduction 
of  leakage  current  can  be  obtained  by  the  use  of  several 
insulated  negative  feeders  of  such  cross  section  that  the 
average  potentials  at  their  feeding  points  are  maintained 
20 


12345 
NUMBER  OF  NEGATIVE  FEEDERS 
Fig.  69. 

equal,  the  negative  bus  bar  being  insulated  from  the  ground 
at  the  station. 

If,  in  addition,  use  be  made  of  negative  boosters  in  the 
feeders,  the  potentials  at  the  feeding  points  can  be  main- 
tained uniform  with  that  of  the  negative  bus-bar  even  with 
widely  fluctuating  loads. 

The  amount  to  which  the  original  leakage  current  is 
reduced  by  various  numbers  of  such  negative  feeders  and 
boosters  as  a  percentage  of  what  would  exist  in  the  case 
of  no  feeders,  is  shown  in  Fig.  69. 


THE  DISTRIBUTING   SYSTEM.  l6l 

If  the  contact-conductor  sections  be  supplied  by  individ- 
ual feeders  and  the  current  of  each  be  passed  through  the 
field  exciting  coil  of  the  booster  which  is  connected  to  the 
track  feeder  for  the  corresponding  section,  as  indicated  in 
Fig.  70,  the  potential  of  the  track  feeding  points  can  be 
kept  practically  equal  to  that  of  the  negative  bus  at  the 
station.  It  should  be  noted  that  the  track  rails  are  insu- 
lated from  the  negative  bus.  This  arrangement  of  connec- 


NEGATIVE  TRACK  FEEDERS 
Fig.  70. 

tions  is  the  most  effective  one  for  minimizing  electrolytic 
corrosion  in  those  systems  which  return  current  through 
the  grounded  track  rails. 

56.  Electrolytic  Surveys.  —  The  determination  as  to 
whether  and  to  what  extent  track  feeders  shall  be  installed 
depends  upon  the  conditions  which  result  from  the  opera- 
tion of  a  road.  These  conditions  are  usually  found  by  mak- 
ing an  electrolytic  survey  and  studying  the  results  thereby 
attained.  The  difference  of  potential  between  the  tracks 
and  the  various  pipe  systems  is  measured  at  many  points 
throughout  the  roadway.  Care  must  be  taken  that  good 
terminal  contacts  be  secured,  for  these  differences  seldom 
amount  to  more  than  a  few  volts.  Upon  a  map,  which 
clearly  shows  all  the  tracks,  the  potential  differences  are 
plotted  as  ordinates  with  respect  to  the  track  as  abscissae, 
and  a  curve  is  drawn  through  their  ends.  Wherever  the 


162  TRACTION    AND  TRANSMISSION. 

track  is  positive  with  respect  to  the  pipe  the  area  included 
between  the  curve  and  the  track  is  generally  colored  blue. 
In  case  it  be  negative  the  area  is  colored  red,  indicating 
that  the  potential  conditions  at  such  places  are  favorable 
to  corrosion  of  the  pipes. 

Another  map  is  prepared  from  which  the  tracks  are 
omitted  but  upon  which  the  pipe  system  under  investi- 
gation is  indicated.  The  magnitude  and  direction  of  the 
currents  flowing  in  the  pipes  at  various  points,  especially  in 
the  red  districts,  are  obtained  and  are  indicated  on  this  map 
by  arrows  of  proportionate  length  and  direction.  Currents 
may  be  measured  by  the  drop-of-potential  method,  using 
a  low-reading  milli voltmeter.  The  portion  of  the  pipe  over 
which  the  drop  is  to  be  obtained  must  be  insulated  from  the 
earth  and  therefore  excavations  are  generally  necessary. 
A  study  of  this  map  is  likely  to  reveal  the  location  of  points 
where  electrolytic  corrosion  is  likely  to  take  place.  Thus, 
if  at  two  points  on  an  unbranched  pipe  currents  be  simul- 
taneously flowing  towards  each  other,  the  conclusion  is 
inevitable  that  they  both  leave  the  pipe  at  an  intermediate 
point.  Again,  if  a  large  current  flow  towards  a  point  where 
a  smaller  one  is  flowing  in  the  same  direction,  the  excess 
of  the  former  must  leave  the  pipe  at  intermediate  points. 

A  relatively  high  potential  difference  between  a  track 
and  pipe  does  not  necessarily  indicate  that  a  large  current 
is  flowing  between  them,  for  such  would  not  be  the  case 
if  the  resistance  offered  by  the  soil  were  large.  It  may  be 
desirable  to  know  whether  the  current  be  large  or  not,  and 
this  can  be  determined  by  the  use  of  Haber's  earth  ampere- 
meter. It  consists  of  a  wooden  frame  in  which  is  mounted 
a  plate  of  glass  with  a  copper  plate  on  each  side  of  it.  The 
free  surfaces  of  the  latter  are  covered  with  a  thin  layer  of 


THE   DISTRIBUTING    SYSTEM. 


163 


paste,  made  of  copper  sulphate  and  20%  sulphuric  acid, 
and  held  in  place  by  parchment.  This  frame  is  buried  in 
the  soil  transverse  to  the  supposed  path  of  current  flow. 
Leads  from  the  copper  plates  are  connected  with  a  milli- 
amperemeter  which  will  indicate  the  flow  of  current  through 
the  soil.  The  device  is  non-polarizable,  and  experience 
shows  that  its  presence  in  the  soil  does  not  distort  the 
current  flow-lines. 

In  order  to- make  the  current  measurements  it  is  neces- 
sary to  know  the  resistance  per  unit  length  of  the  pipe. 
This  may  be  obtained  from  the  following  table  published 
by  Prof.  A.  F.  Ganz,  based  upon  a  specific  resistance  of 
0.00144  ohm  per  pound-foot  of  cast  iron  and  0.000181  ohm 
per  pound-foot  of  wrought-iron  pipe. 

WEIGHT  AND  RESISTANCES  OF  CAST-  AND  WROUGHT-IRON  PIPE. 


Standard  cast  iron. 

Standard  wrought 
iron. 

Extra  heavy  wrought 
iron. 

Inside 

diameter 

of  pipe, 
inches. 

Weight 
per  foot 
without  hub 
pounds. 

Resistance 
per  foot, 
ohms. 

Weight 
per  foot 
without  hub 
pounds. 

Resistance 
per  foot, 
ohms. 

Weight 
per  foot 
without  hub 
pounds. 

Resistance 
per  foot, 
ohms. 

\ 

.84 

.000215 

I  .  I 

.000164 

I 

i-7 

.000106 

2.  2 

.000082 

li 

2-7 

.000067 

3-6 

.  0000502 

2 

3.6 

.  0000502 

5- 

.0000362 

3 

II. 

.000131 

7-5 

.0000241 

10. 

.0000181 

4 

18. 

.000080 

10.6 

.0000171 

15- 

.OOOOI  2  I 

6 

31- 

.0000465 

18.8 

.  00000963 

29. 

.00000623 

8 

42. 

.0000343 

28. 

.00000647 

43- 

.OOOO042I 

10 

55- 

.OOOO262 

40. 

.  0000045  2 

54- 

.00000335 

12 

70. 

.OOOO2O6 

49- 

.00000369 

65. 

.00000278 

16 

109. 

.0000132 

18 

130. 

.  OOOOI  I  I 

20 

151- 

.00000955 

24 

205. 

.00000702 

30 

294. 

.00000490 

36 

408. 

.00000353 

48 

604. 

.00000238 

164  TRACTION  AND  TRANSMISSION. 

57.  Alternating-current  Distribution. — The  voltage  drops 
which  occur  with  alternating-current  systems  are  dependent 
not  only  upon  the  resistances  of  the  conductors  but  also 
upon  their  reactances  and  the  phases  of  the  components  of 
current.  An  adequate  general  treatment  of  the  subject 
is  out  of  place  in  this  text.  The  methods  of  determin- 
ing line  reactances  will  be  given  in  a  later  chapter.  The 
flexibility  and  cheapness  of  transformers  permit  of  their 
extensive  use  for  the  equalization  of  potentials,  whereas 
excessive  copper  or  boosters  are  essential  in  direct-current 
systems. 

The  high  permeability  and  the  hysteresis  characteristics 
of  steel  track  and  third  rails  involve  large  drops  when  they 
carry  alternating  currents.  Skin  resistance  becomes  an 
important  factor  and  it  has  been  estimated  that  at  frequen- 
cies of  15  and  25  the  current  confines  itself  to  a  peripheral 
depth  of  but  4  and  3  millimeters  respectively.  Disregarding 
any  drop  due  to  flux  set  up  outside  the  rail,  its  impedance, 
according  to  Armstrong,  is  8  times  the  ohmic  resistance  at 
25  cycles  and  6.2  times  at  15  cycles. 

PROBLEMS 

31.  Calculate  the  resistance  at  20°  Centigrade  of  a  30-foot  length  of  track 
rail  weighing  700  pounds.     Take  7.7  as  the  specific  gravity  of  steel  rail. 

32.  How  far  from  the  terminus  of  a  road  is  the  last  feeding  point  to  a 
No.  oooo  copper  contact  conductor  supplying  o.oi  ampere  per  foot,  if  the 
potential  at  the  feeding  point  is  maintained  at  550  volts  and  the  drop  in 
the  contact  conductor  must  not  exceed  20  per  cent? 

33.  The  two  cross-bonded  contact  conductors  of  the  Manhattan  Ele- 
vated Railroad  consist  of  third  rails  weighing  100  Ibs.  per  yard.     They  are 
fed  at  both  ends  from  substations  which  maintain  a  constant  potential  of 
625  volts.     If  the  distance  between  substations  be  one  mile  and  the  current 
drainage  from  both  tracks  at  maximum  load  be  0.3  ampere  per  foot,  what 
is  the  maximum  percentage  drop  in  the  contact  conductors? 

34.  Determine  the  economic  cross-section  of  a  copper  feeder  to  carry 


THE  DISTRIBUTING  SYSTEM.  165 

350  amperes  for  2500  effective  hours  per  year.  Assume  the  cost  of  a  kilo- 
watt-hour as  one  cent,  the  cost  of  a  pound  of  copper  18  cents,  and  the  rate 
of  interest  and  depreciation  as  6  per  cent. 

35.  If  the  feeder  of  problem  34  be  supplied  with  current  at  550  volts, 
what  is  the  greatest  length  which  may  be  used  without  producing  a  drop 
exceeding  ten  per  cent? 

36.  Plot  a  curve,  based  upon  the  constants  given  in  §  53,  which  shows 
the  dependence  of  equivalent  hours  of  operation  upon  the  minimum  feeder 
length  for  economic  installation  of  a  booster  assuming  an  average  booster 
efficiency  of  85  per  cent. 


1 66  TRACTION  AND  TRANSMISSION. 


CHAPTER   VIII. 
SUBSTATIONS. 

58.  Types  of  Substations.  —  A  substation  is  a  station 
which  contains  devices  which  serve  to  alter  the  voltage  or 
character  of  the  current  received  from  the  transmission  line 
and  thereafter  deliver  it  to  the  distributing  system.     Sub- 
stations are  of  three  types,  depending  upon  the  character 
of  the  received  and  delivered  currents  as  to  whether  they 
are  direct  or  alternating. 

59.  Direct  Currents  Received   and   Delivered.  —  With 
the  Thury  system,  which  is  employed  to  some  extent  in 
Europe  but  which  is  not  looked  upon  with  favor  by  Amer- 
ican engineers,  direct  current  is  generated  at  the  power 
house,   transmitted   and  received  at   the   substation  and 
direct  current  is  sent  out  from  the  substation.     A  typical 
example  of  this  system  is  the  plant  which  transmits  power 
from  Moutiers  in  Savoy  to  Lyons  for  the  operation  of  the 
street  railways  in  the  latter  city.     Sixteen  water-turbine- 
driven  direct-current  generators,  consisting  of  four  sets  of 
four  each,  are  connected  in  series  with  each  other  and  can, 
at  full  load,  generate  3500  volts  each  or  56,000  volts  in  all. 
They  supply  a  constant  current  of  75  amperes  to  the  line, 
and  their  voltage  is  varied  with  the  load  by  means  of 
electrically  operated  regulators  connected  in  series  with  the 
line.     The  sets  may  be  operated  singly  or  together  accord- 
ing to   the  load  requirements,  a   single  movement  of  a 
controller  handle  on  a  simple  switchboard  serving  to  cut  in 


SUBSTATIONS.  l6/ 

or  out  a  set.  The  transmission  line  is  no  miles  long,  con- 
sists of  two  copper  wires  0.354  inch  in  diameter,  and 
entails  a  constant  loss  of  535  kilowatts.  It  has  been  found 
necessary  to  keep  the  line  connected  to  the  earth  through 
high  resistances  and  to  provide  numerous  lightning  arresters. 
At  the  substation  the  received  current  is  used  to  operate 
motors  each  of  540  horsepower  capacity.  The  speed  of 
the  motors  is  maintained  constant  by  centrifugal  regula- 
tors which  shift  the  brushes  when  the  load  changes.  These 
regulators  are  criticized  as  being  an  inherent  defect  of  the 
system,  for  they  are  complicated  and  frequently  require 
adjustment  and  repairs.  Each  motor  is  used  to  drive  a 
6oo-volt  direct-current  generator  which  is  connected  with 
the  distributing  system.  Special  precautions  are  taken 
to  insulate  the  motors  from  each  other,  from  the  earth, 
and  from  the  generators  which  they  drive.  Tests  have 
shown  that  the  power  output  of  the  substation  is  0.705 
that  of  the  intake  of  the  turbines  which  drive  the  generators 
at  the  power  house.  As  a  precaution  against  breakdown 
of  the  line  or  power  station,  the  substation  is  amplified  by 
an  auxiliary  transformer  station  in  which  direct-current 
motors  are  direct  connected  to  io,ooo-volt  three-phase 
generators,  the  latter  being  adapted  for  connection  with 
the  lines  of  another  operating  company.  These  sets  are 
reversible  and  by  means  of  them  energy  may  be  supplied 
to  or  received  from  the  other  system.  The  power  stations 
and  the  substations  in  this  direct-current  system  cost  more 
than  those  which  use  alternating  currents  for  transmission. 
The  cost  of  the  transmission  line  is  less  and  the  maximum 
voltage,  as  limited  by  the  appearance  of  corona,  §  72,  is 
greater.  The  system  is  lacking  in  that  flexibility  which 
characterizes  the  use  of  transformers. 


i68 


TRACTION   AND   TRANSMISSION. 


60.   Alternating  Currents  Received  and  Delivered.  —  In 

those  systems  which  employ  induction  motors  on  the  cars 
or  locomotives,  three-phase  currents  are  generated  at  the 
power  station,  and,  if  the  length  of  the  transmission  line 
requires  more  than  an  impressed  voltage  of  12,000  —  the 
upper  voltage  limit  of  generators  —  at  least  three  single- 
phase  step-up  transformers  or  one  three-phase  transformer 
must  be  used.  At  the  substation  three  step-down  trans- 
formers must  be  located,  and  usually  a  fourth  one  is  in- 
stalled as  a  spare  unit.  Such  substations  are  designed  to 


1.00 


>-"0.99 
o 

z 

LJ 

5 

u. 
uiO.98 


0.97 


250  500 

CAPACITY  IN  KILOWATTS. 
Fig.  71. 


750 


operate  without  an  attendant  and  therefore  the  transformers 
are  self-cooling  and  both  the  primary  and  secondary  circuits 
are  supplied  with  automatic  oil  switches  adjusted  to  open 
on  short  circuits  but  not  on  overloads.  Fig.  71  shows  the 
full-load  efficiencies  of  a  line  of  25-cycle,  n,ooo-volt  air- 
blast  transformers  of  capacities  from  100  K.W.  to  750 
K.W.  The  buildings  are  of  fireproof  construction,  and 
permanently  installed  ammeters  and  voltmeters  facilitate 
the  location  of  possible  faults  on  the  system. 

In  those  systems  which  employ  single-phase  commutator 


SUBSTATIONS.  169 

motors,  if  the  transmission  line  be  single  phase  and  be 
long,  and  consequently  the  voltage  be  high,  but  one  step- 
up  and  one  step-down  transformer  are  necessary.  Since, 
however,  it  is  cheaper  to  use  a  three-phase  transmission 
line  it  is  advisable  to  use  a  three-phase  generator  and  three 
step-up  transformers  at  the  power  station  and  two  step- 
down  transformers  at  the  substation,  the  latter  being  con- 
nected according  to  Scott's  method  for  transformation 
from  three-phase  to  two-phase  with  connections  as  shown 
in  Fig.  12.  Furthermore,  the  cost  per  kilowatt  of  three- 
phase  generators  is  but  about  three-quarters  that  of  single- 
phase  generators,  because  in  the  former  a  single  magnetic 
circuit  is  used  in  common  by  all  phases. 

Experience  has  shown  that  it  is  practicable  to  use 
alternating-current  pressures  as  high  as  20,000  volts  on 
overhead  contact  conductors.  In  such  cases  stationary 
substations  may  be  dispensed  with,  and  voltage  reduction, 
suitable  to  the  requirements  of  the  motors,  can  be  attained 
by  the  use  of  transformers  located  on  the  cars  or  locomo- 
tives. In  some  respects  this  arrangement  is  ideal,  each 
motor  having  a  substation  and  carrying  it  with  it.  There 
are  no  substations  on  the  electrically  equipped  portion  of 
the  N.  Y.  N.  H.  &  H.  R.R.,  11,000  volts  being  generated 
and  impressed  directly  upon  the  contact  conductors  of  the 
system.  Each  motor,  however,  is  provided  with  a  trans- 
forming device.  The  locomotives  used  in  the  Berlin- 
Zossen  tests  were  equipped  with  polyphase  motors  wound 
for  an  impressed  pressure  of  10,000  volts  taken  direct  from 
the  contact  conductors  without  the  intervention  of  voltage 
transforming  devices. 

61.  Alternating  Currents  Received  and  Direct  Cur- 
rents Delivered.  —  Substations  which  convert  alternating 


1 70  TRACTION  AND   TRANSMISSION. 

current  into  direct  current  are  the  type  most  frequently 
used.  By  means  of  transformers  the  voltage  of  the  currents 
received  from  the  transmission  line  is  stepped  down  and  the 
secondary  currents  are  supplied  to  converters  or  motor- 
generators  which  deliver  direct  currents  to  the  distribut- 
ing system.  The  motor  element  of  the  motor  generators 
may  be  either  a  synchronous  motor  or  an  induction  motor. 
The  proper  selection  of  the  conversion  apparatus  involves 
a  number  of  considerations. 

Floor  Space.  —  In  all  cases  it  is  customary  to  install 
three  single-phase  transformers  or  one  three-phase  trans- 
former for  each  converter.  Since  both  induction  and  syn- 
chronous motors  are  wound  for  an  impressed  E.M.F.  up 
to  12,000  volts,  step-down  transformers  can  usually  be 
dispensed  with.  Even  then  the  floor  space  occupied  by 
converters  and  transformers  is  less  than  that  required  for 
equivalent  motor-generators.  Wilson  and  Lydall  give  the 
following  values  for  units  of  about  750  K.W.  capacity: 

Converters  and  transformers,  0.21  sq.  ft.  per  K.W. 
Induction  motor-generators,  0.31  sq.  ft.  per  K.W. 

The  possible  separate  location  of  converters  and  trans- 
formers, for  instance  the  placing  of  transformers  on  a 
gallery,  gives  a  flexibility  of  arrangement  of  apparatus  not 
possessed  by  motor-generators.  With  urban  substations 
and  expensive  real  estate  the  occupied  floor  space  becomes 
an  important  factor. 

Efficiency.  —  The  efficiency  of  synchronous  converters  is 
greater  than  that  of  motor-generators.  Even  if  to  the 
losses  of  the  converters  be  added  the  losses  in  transformers 
and  regulating  devices,  which  are  not  involved  in  the  use  of 
motor-generators,  the  efficiency  of  the  combined  converter 


SUBSTATIONS. 


I/I 


installation  excels.     W.  R.  C.   Corson  gives  the  average 
operating  efficiencies  from  this  point  of  view  as  follows: 

Synchronous  converters Qi% 

Synchronous  motor-generators 85% 

Induction  motor-generators 84% 

Figs.  72  and  73  contain  curves  showing  the  operating 
characteristics  of  a  shunt- wound,  25-cycle,  6oo-K.W.conver- 


2500 


0         25         50         75        100       125       150        175      200 

PER  CENT,  OF  FULL  LOAD  CURRENT 

FROM  COMMUTATOR 

Fig.  72. 

ter,  and  of  a  5o-cycle,  230-K.W.  induction  motor-generator 
respectively. 

Regulation.  —  Since  the  ratio  between  the  commutator 
and  slip-ring  voltages  of  a  converter  is  practically  constant, 
irrespective  of  the  field  excitation,  except  in  the  case  of 
split-pole  converters,  it  is  customary  to  insert  a  reactance 
coil  in  the  circuit  between  the  low-tension  terminal  of  a 


1/2 


TRACTION   AND   TRANSMISSION. 


transformer  and  the  converter  slip  ring  which  it  supplies 
with  current,  and  to  provide  the  converter  with  a  series 
magnetizing  coil  which  is  traversed  by  the  direct  current 
from  the  commutator  before  it  enters  the  feeders  of  the 
distribution  circuit.  The  field  excitation  is  thereby  caused 
to  increase  with  load,  and  the  alternating  current  which 
enters  the  slip  rings  is  therefore  made  to  lead  the  impressed 
voltage.  The  passage  of  the  leading  current  through  the 
reactance  coil  establishes  such  phase  relation  that  the  vector 


100  200  300 

LOAD  IN  KILOWATTS, 

Fig.  73- 


400 


sum  of  the  transformer  and  reactance  voltages  is  greater 
than  the  former  and  therefore  the  slip-ring  voltage  is  raised 
with  load.  The  converter  with  such  an  arrangement  is 
said  to  be  compounded,  and  may  maintain  a  constant  direct- 
current  voltage  under  wide  variations  of  load.  It  is 
usual  to  provide  for  each  phase  a  reactance  coil  of  a 
combined  kilo  volt-ampere  capacity  equal  to  15  %  of  the 
rated  kilowatt  capacity  of  the  corresponding  converter. 
Fig.  74  shows  a  General  Electric  Company  air-blast  reac- 
tance set  and  starting  switches  for  a  iooo-K.W.,  six-phase 
converter.  The  operating  characteristics  of  the  6oo-K.W. 


SUBSTATIONS.  1/3 

converter  previously  mentioned,  with  added  series  ampere- 
turns  at  full  load  amounting  to  64  %  of  the  shunt  ampere- 
turns,  are  shown  in  Fig.  75.  With  proper  adjustments  of 
the  series  and  shunt  field  coils  it  is  possible  to  make  the 
converter  take  a  lagging  current  on  light  loads  and  a  leading 
current  on  heavy  loads.  It  therefore  increases  the  power 


Fig.  74- 

factor  of  the  transmission  circuit  on  heavy  loads.  This 
method  of  regulation,  however,  fails  to  give  satisfactory 
results  when  the  line  resistance  drop  exceeds  10  %  of  the 
impressed  line  voltage  or  even  less;  and  yet  on  large  trans- 
mission systems  and  with  long  transmission  lines  it  is  desir- 
able and  often  economical  to  have  a  drop  greater  than  this. 
With  motor-generators,  however,  the  direct-current  volt- 
age can  be  as  easily  and  satisfactorily  regulated  as  with 


174 


TRACTION  AND   TRANSMISSION. 


plain  generators,  and  the  regulation  is  in  nowise  dependent 
upon  the  drop  in  the  transmission  line.  Furthermore,  by 
the  use  of  series  coils  on  a  synchronous  motor  field  the 
motor-generator  set  may  be  adapted  for  power  factor  correc- 
tion to  the  same  extent  as  with  converters. 

Cost.  —  The  cost  of  converters  per  se  is  less  than  that  of 
motor-generators  of  the  same  capacity.     Compound  con- 

lOOi 1 1 — ^  i  ' 1 1 1 1 i2500 


0         25         50         75        100       125        ISO       175      200 

PER  CENT,  OF  FULL  LOAD  CURRENT 

FROM  COMMUTATOR 

Fig.  75- 

verters  cost  more  than  shunt  converters  because  of  the 
lower  flux  density  in  the  iron. 

To  make  a  proper  comparison  of  the  costs  of  the  two 
types  of  installation  one  should  consider  the  whole  system 
and  compare  the  total  cost  of  converters,  regulating  devices, 
transformers,  switch  gear,  ventilation  apparatus,  and  trans- 
mission cables  with  that  of  equivalent  motor-generators, 
switch  gear,  and  cables.  Parshall  and  Hobart  make  such  a 


SUBSTATIONS. 


175 


comparison  for  a  plant  supplying  three  substations  each 
having  a  rated  output  of  1800  K.W.,  the  most  remote  being 
6  miles  from  the  power  house.  The  results  are  given  in 
the  following  table. 

RELATIVE   COSTS  OF  CONVERSION  INSTALLATIONS 


Converters. 

Motor 
generators. 

High-tension  cables    

$8o,000 

$55,OOO 

Converters  (6-900  K  W  ) 

67.coo 

Miotor  generators 

Il8,OOO 

Transformers  and  ventilating  sets  (21-300 
K  W  ) 

31x00 

Substation  switchboards  and  gear 

27,000 

l8,OOO 

Total                                 

$206,000 

$191,000 

The  smaller  cable  expenditure  with  motor-generators 
results  from  their  ability  to  operate  satisfactorily  with  a 
greater  line  drop  than  is  allowable  with  converters.  Whether 
the  interest  on  the  7  %  less  outlay  with  motor-generators 
would  offset  the  increased  operating  cost  resulting  from 
the  smaller  efficiency  of  the  motor-generators  would  require 
a  careful  study  of  the  substation  load  diagrams.  The  pre- 
ceding table  is  based  upon  the  following  costs  per  rated 
kilowatt : 

Converters $12.50 

Transformers  and  ventilation  apparatus 5.00 

Converter  switch  apparatus 5.00 

Motor-generators 21.90 

Motor-generator  switch  apparatus 3.33 

The  data  concerning  the  converter  equipment  relate  to 
an  existing  substation. 

62.  Location  of  Substations.  —  There  are  certain  points 
on  the  roadway  of  a  traction  system  which  may  be  con- 
sidered as  natural  points  for  the  location  of  a  substation. 


TRACTION   AND   TRANSMISSION. 

These  are  the  centroids  of  load  in  urban  networks,  the 
power  house  when  it  is  located  on  the  line,  and  the  middle 
or  a  point  near  the  remote  ends  of  the  terminal  sections 
of  the  lines.  It  is  also  often  desirable  to  have  the  substation 
located  at  a  passenger  station,  thus  making  it  possible  for 
the  ticket  agent  to  serve  as  a  substation  attendant. 

If  it  be  assumed  that  there  is  a  uniform  drainage  of  cur- 
rent throughout  the  length  of  the  road  and  that  the  con- 
tact conductor  has  numerous  connections  with  the  supple- 
mentary conductor,  the  composite  conductor,  of  uniform 
cross  section,  extending  from  one  substation  to  each  adja- 
cent substation,  then  the  economic  distance  between  sub- 
stations can  be  determined  by  mathematical  treatment. 


COMPOSITE  CONTACT  CONDUCTOR 


Fig.  76. 

Furthermore,  if  the  profile  of  the  road  be  such  that  along 
certain  portions  the  drainage  of  current  is  greater  than 
along  the  rest  of  the  line,  each  portion  by  itself  can  be 
treated  mathematically. 

Assume  a  road  of  length  L  feet  to  be  supplied  with  cur- 
rent from  n  substations,  equally  spaced  from  each  other 
by  a  distance  X  =  L/n  feet,  and  arranged  as  in  Fig.  76, 
where  the  substations  are  represented  by  S. 

The  annual  mean  effective  current  per  foot  of  contact 
conductor  can  be  determined  from  a  study  of  the  train 
diagrams  and  from  the  instantaneous  currents  per  car. 
The  maximum  drop,  which  will  occur  at  a  point  midway 


SUBSTATIONS. 

between  substations  and  at  the  terminals  of  the  line,  is 
limited  to  such  a  value  as  will  permit  satisfactory  operation 
of  the  motors  and  lighting  of  the  lamps,  is  known,  and 
must  be  used  as  a  check  on  the  economic  drop  about  to  be 
determined.  See  problem  No.  37. 

For  a  fixed  distance  between  substations,  the  economic 
cross  section,  A,  for  the  composite  contact  conductor,  is 
such  that  the  annual  charge  for  interest  and  depreciation 
on  its  cost  is  equal  to  the  annual  charge  for  the  energy  lost 
in  it.  To  prove  this,  consider  that  the  former  charge  is 
dependent  on  the  weight  of  the  conductor,  that  is  its  cross 
section,  and  may  be  placed  equal  to  K\A ,  and  the  latter  on 
the  resistance,  which  may  be  placed  equal  to  ,K$/A,  where 
KI  and  K2  are  constants.  The  sum  of  these  two  charges, 
Xj  must  be  a  minimum,  hence  the  differential  of  x,  with 
respect  to  A,  must  equal  zero.  Therefore 

dx       „       K2 
-=Kl--  =  o      . 

and 

KiA  =  K2/A  dollars.  (i) 

If  now,  with  a  conductor  of  constant  cross  section,  the 
distance  between  the  substations  be  increased,  which  is 
equivalent  to  reducing  the  number  of  substations  for  a 
road  of  given  length,  the  resistance  and  weight  of  the  con- 
ductor between  stations  will  be  increased  proportionately. 
The  interest  charge  will  likewise  increase,  while  the  energy 
charge  will  increase  to  a  greater  extent,  because  the  current 
entering  the  section  of  conductor  from  the  substation  has 
also  been  increased.  Therefore  KZ/A  is,  in  this  case,  larger 
than  KiA,  and  to  maintain  the  equality  of  equation  (i) 
the  value  of  A  must  be  increased. 


173  TRACTION  AND   TRANSMISSION. 

The  increase  of  distance  between  substations,  or  reduc- 
tion in  their  number,  furthermore  affects  the  charges  for 
interest,  maintenance,  and  operation  of  all  the  substations. 
The  wages  for  fewer  attendants  and  the  costs  and  losses 
per  kilowatt  of  the  larger  units  installed  are  thereby  de- 
creased. The  economic  cross  section  of  contact  conductor 
and  economic  distance  between  substations,  therefore,  in- 
volves a  minimum  annual  charge  for  wages,  for  interest  on 
total  cost  of  copper  and  equipment,  and  for  cost  of  total 
energy  lost  in  copper  and  equipment.  Expressions  for 
each  of  these  items  of  annual  charge  must  be  found  in 
terms  of  the  distance,  X,  between  substations,  and  the 
differential  coefficient  of  their  sum,  with  respect  to  X,  must 
be  equated  to  zero  in  order  to  determine  the  economic 
separation  of  substations. 

It  will  be  assumed  that  the  annual  charges  against  the 
transmission  line,  the  energy  lost  in  the  track,  and  the  cost 
of  substation  buildings  are  not  affected  by  changes  in  X. 
The  last  two  charges  can  be  introduced  without  difficulty, 
if  desired.  The  first  charge  materially  alters  with  X  only 
in  the  case  of  very  short  lines  and  very  heavy  traffic. 

Wages.  —  For  a  given  type  of  substation,  length  of  line 
and  density  of  traffic,  the  necessary  number  of  attendants 
in  each  substation  and  their  average  wages  will  not  vary 
with  the  size  of  the  units,  so  far  as  these  sizes  are  dependent 
upon  X.  For  all  substations,  however,  they  will  vary 
directly  with  the  number  of  substations,  n  =  L/X,  and  if 
there  be  n'  attendants  per  substation,  receiving  on  an 
average  w'  dollars  per  year,  the  total  annual  charge  for 
attendants 

Cw  =  nn'w'  =  [riw'L}\-  (2) 

A 


SUBSTATIONS.  1/9 

With  transformer  substations  there  are  no  attendants  and 
therefore  Cw  becomes,  in  this  case,  zero. 

Charges  against  Contact  Conductor.  —  Consider  that  part 
of  the  contact  conductor  of  cross  section  A  circular  mils 
which  is  fed  from  one  substation.  Under  the  assumption 
of  a  uniform  drainage  of  /o  mean  effective  amperes  per  foot, 
the  watts  lost  in  each  half  of  the  conductor,  or  X/2  feet,  are, 
according  to  equation  (5),  §  48,  p/02X3/24^4.  There  being 
8760  hours  in  a  year,  at  a  cost  of  c$  dollars  per  kilowatt- 
hour  delivered  from  the  substation,  the  annual  charge  for 
the  energy  lost  in  X  feet  of  the  conductor  is 


C.'  =  -       If*  dollars.  (3) 

IOOO   12.4 

If  the  cost  of  conductor  be  c2  dollars  per  pound  and  w  be 
the  weight  of  a  mil-foot  in  pounds,  at  an  interest  rate  of  p% 
the  annual  capital  charge  against  the  contact  conductor  is 
Cc"  =  p^wA\  dollars.  (4) 

Since  Cc'  must  equal  Cc"  when  the  cross  section  A  is  most 
economical,  equations  (3)  and  (4)  may  be  equated  and 
solved  for  A  as  follows: 

A  =  0.855  /oXy    P  3     circular  mils.  (5) 

V         CW 


Substituting  the  value  of  A  in  (4),  multiplying  by  2  so 
as  to  include  Cc'  and  by  L/\  =  n  to  cover  the  whole  length 
of  line,  the  total  annual  charge  against  contact  conductor  is 


or  Cc=  [1.71  L/o  Vpwp2c2C3\\  dollars.  (6) 

Annual  Charge  against  Substations.  —  If  the  total  max- 
imum output  of  all  substations  be  P  kilowatts  and  if  the 


180  TRACTION  AND   TRANSMISSION. 

overload  coefficient  or  ratio  of  maximum  output  to  rated 
installed  capacity  be  6,  then  the  rated  capacity  of  the  appa- 
ratus installed  in  each  substation  is  P/dn  K.W.  The  over- 
load coefficient  is  determined  from  a  study  of  the  nature 
of  the  load  diagram  for  each  substation  and  from  the  over- 
load guarantees  as  to  the  apparatus.  In  determining  the 
number  of  units  to  be  installed  in  each  substation  the  fol- 
lowing points  must  be  considered : 

(a)  It  is  desirable  and  good  practice  to  have  the  same 
sized  units  throughout  the  system  whenever  possible. 

(b)  There  are  limits  as  to  the  maximum  size  of  units 
to  be  found  among  manufacturers'  standard  lines. 

(c)  The  daily  load  curve  is  often  of  such  a  character 
that  one  unit  and  several  units  can  be  operated  for  pro- 
tracted intervals  at  nearly  maximum  efficiency. 

(d)  The  maintenance  of  the  continuity  of  service  requires 
that  either  a  spare  unit  be  installed  in  each  substation  or 
that  there  should  be  a  portable  substation  which  can  be 
placed  on  a  siding  as  needs  may  require. 

(e)  The  peak  of  the  load  may  be  taken  by  a  storage 
battery  installed  in  each  substation. 

(/)  Provision  must  be  made  for  increased  output  with 
growth  of  traffic. 

Fig.  77  shows  the  load  curve  on  No.  2  substation  of  the 
Manhattan  Division  of  the  Interborough  Rapid  Transit 
Company  for  July  13,  1903.  This  substation  was  equipped 
with  six  I50O-K.W.  converters  each  having  efficiencies  of 
93.5,  95.75,  and  96.0  per  cent  at  half,  full,  and  five-quarters 
load  respectively.  They  were  supplied  with  alternating 
current  from  eighteen  550-K.W.  transformers,  three  for 
each  converter,  each  having  efficiencies  of  97,  97.75,  and 
97.7  per  cent  respectively  at  the  corresponding  loads. 


SUBSTATIONS. 


S 


o 
o 

•SJJ.VMOTLM 


182 


TRACTION  AND   TRANSMISSION. 


Assuming  that  the  overload  capacities  are  as  recommended 
in  the  Standardization  Rules  of  the  A.I.E.E.,  that  is,  that 
they  can  each  carry  an  overload  of  25  %  for  two  hours  and 
50  %  for  one-half  hour,  the  load  diagram  shows  the  prob- 
able operating  conditions  of  these  units  on  this  day  to  be 
as  in  the  accompanying  table,  the  numbers  in  the  third 
column  indicating  the  equivalent  number  of  hours  that  a 
unit  must  be  operated  at  full  load  in  order  that  its  losses 
may  be  the  same  hypothetically  as  they  are  in  fact.  To 
determine  the  equivalent  hours,  if  the  efficiency  at  any  load 
be  e,  let  the  expression  (i  —  e)  be  termed  the  deficiency  at 
that  load;  then  the  equivalent  hours  are  equal  to  the  pro- 
duct of  the  number  of  hours  at  any  load  by  the  ratio  of  that 
load  times  its  deficiency  to  full  load  times  its  deficiency. 

CONDITIONS  OF  OPERATION   OF  UNITS 


Unit. 

Hours  per  day. 

Equivalent 
hours  per  day. 

No.  i 

24 

21.4 

No.  2 

15-5 

15-0 

No.  3 

8.8 

7-5 

No.  4 

2.O 

2.0 

No.  5 

O 

0 

No.  6 

0 

0 

Total  daily  equivalent  unit,  hours,  45.9 

The  equivalent  annual  hours  of  operation  of  all  units 
in  this  substation  at  full  load  are  therefore 


h  = 


6 


=  2792  hours. 


The  load  on  this  substation  was  about  20  %  greater  in 
winter  than  as  shown  in  Fig.  77,  due  partly  to  the  current 
required  for  car  heaters.  Instantaneous  fluctuations  of 


SUBSTATIONS. 


183 


current  above  and  below  those  shown  in  the  figure  amounted 
in  some  cases  to  40  %.  In  calculating  losses  in  a  proposed 
substation  a  mean  effective  load  diagram  should  be  used. 

To  obtain  an  expression  for  the  annual  charge  for  energy 
lost  in  the  substation  in  terms  of  X,  it  is  necessary  to  plot 
deficiency  curves  in  terms  of  the  rated  capacity  of  units. 
There  should  be  say  three  curves,  for  half,  full,  and  three- 
halves  load  respectively.  The  points  on  these  curves  can 


CONVERTER -TRANSFORMER  UNITS. 


500 


1000 


CAPACITY,  P0>   IN   KILOWATTS. 
Fig.  78. 


1500 


2000 


be  obtained  readily  from  manufacturers'  efficiency  curves  of 
units  for  say  three  rated  capacities,  as  500,  1000,  and  1500 
kilowatts.  Three  such  curves  for  combined  transformer- 
reactance-converter  units,  at  unity  power  factor,  are  shown 
in  Fig.  78.  The  full-load  curve  is  practically  straight  over 
the  portion  covered  by  the  capacities  entering  into  the 
problem,  and  the  deficiency,  3,  may  be  expressed  analyti- 
cally as 

5=/3-£3Po,  (7) 

where  PQ  is  the  rated  capacity  in  kilowatts. 


1 84 


TRACTION  AND   TRANSMISSION. 


The  following  values  are  suggestive  of  the  order  of  magni- 
tude of  the  cons  tan  ts/3  and  #3  for  conversion  at  25  cycles 
from  11,000  volts  to  600  volts: 


DEFICIENCY   CONSTANTS 


Units. 

K.W. 

/3. 

£3- 

Transformer-  reactance-converter 
Transformer-  reactance-converter 
Transformers  . 

500  to  2000 
200  to    500 
100  to    750 

0.072 

0.087 

o  024 

0  .  OOOOI  2 

o  .  000060 
o  oooo  i  4 

The  converters  of  larger  capacity  listed  in  the  table  are 
wound  six-phase,  while  those  of  smaller  capacity  are  three- 
phase.  If  there  be  u  units  of  capacity  P0  kilowatts  in- 
stalled in  each  substation,  including  spare  units,  and  h  be 
the  equivalent  annual  hours  of  operation  of  all  units  at  full 
load,  then,  since  P0  =  P/5nu,  the  annual  loss  of  energy  in  all 
substations  is 


52nu 


kilowatt-hours. 


(8) 


Since  n  =  L/X,  if  the  cost  per  kilowatt-hour  of  energy 
delivered  to  the  substation  be  c^  dollars,  the  annual  charge 
against  the  substations  for  energy  lost  in  them  is 


(9) 


The  cost  of  one  unit  of  capacity  P0  kilowatts  can  be 
expressed  analytically  as  /3'  +  gz'PQ  dollars,  where  /3'  and 
g3'  are  constants  determined  by  the  manufacturer.  The 
cost  of  all  units  to  be  installed  in  all  substations  is  therefore 
nu(fz  +Pgs'/dnu),  and,  if  pz  be  the  annual  rate  covering 
interest,  depreciation,  and  obsolescence,  the  annual  charge 
against  cost  of  substation  equipments  is 


SUBSTATIONS. 


185 


C. 

or,  since  n  =  L/X, 

C."  = 


L     o     J 


'«]  7  dollars- 
A 


The  following  values  are  suggestive  of  the  order  of  magni- 
tude of  the  constants  fz  and  g3'. 


COST  CONSTANTS 


Units. 

K.W. 

/•'.. 

g3. 

Transformer-reactance-converter.  .  . 
Transformer-reactance-converter.  .  . 
Transformers  

5OO  tO  2OOO 
200  tO      5OO 

250  to    750 

3200 
2OOO 
240 

9-4 

II.  O 

2.66 

The  total  annual  charge  against  the  substation  equip- 
ments is  equal  to  the  sum  of  C8  and  C8"  as  given  in  equa- 
tions (9)  and  (10),  or  is 


The  Economic  Spacing  of  Substations.  —  The  economic 
value  of  X  is  such  that  the  total  annual  charges  or  the  sum 
of  Cw,  CC1  and  Ca,  as  given  in  equations  (2),  (6),  and  (n), 
shall  be  a  minimum.  To  avoid  needless  repetition  of  the 
letters  entering  into  the  bracketed  coefficients  of  these 
equations,  these  coefficients  may  be  represented  as  follows: 

C,  =  KJ\, 

Cc  =  Kc\, 

C8  =  K8  +  Kaf/\  +  K8'\ 
and  their  sum  as 

C  =  K.+  (KW  +  K8f)/\  +  (Kc  +  #.")  X. 
To  determine  the  minimum  value  of  X,   the  differential 


l86  TRACTION  AND   TRANSMISSION. 

coefficient  of  C,  with  respect  to  X,  must  be  placed  equal  to 
zero,  or 

dC  .         ^  +  K'a 
--          -lr-  + 

Solving, 


c.    =0. 


and  substituting  the  values  of  the  coefficients, 

x=     /  n'™'L  +  W«L  feet.      (13) 


The  economic  cross  section,  A,  for  the  composite  contact 
conductor  can  now  be  obtained  by  inserting  the  value  of  X 
in  equation  (5). 

63.  Numerical  Illustration.  —  For  the  purpose  of  more 
clearly  understanding  the  influence  of  the  factors  entering 
into  the  economic  spacing  of  substations,  assume  a  road 
200,000  feet  long  with  converter  substations  that  are  to 
be  cared  for  by  two  attendants,  each  receiving  $720  per 
annum,  and  each  on  duty  12  hours  each  day,  every  station 
to  be  equipped  with  two  converter  units  of  equal  size.  The 
cost  and  deficiency  constants  will  be  those  applying  to 
units  under  500  K.W.  capacity.  Let  the  following  be  the 
values  of  the  characteristic  constants: 

P/d  =  2500  K.W.,  5  =  1.25, 

/o  =  0.00875  ampere  per  foot,  p2  =  0.06, 

h  =  5000  hours,  ps  =0.10, 

p  =  10  ohms,  c2  =  o.i 8  dollar, 

w  =  0.00000303  pound,  c3  =  €3  =  o.o i. 


SUBSTATIONS. 


I87 


Then 


X  =  ([2  X  720  X  200,000  +0.10  X  2000  X  2  X  200,000] 
-7-1.71  X  0.00875  X  200,000  X 


Vio  X  0.00000303  X  0.06  X  0.18  X  o.oi  + 

/         \2  vx°-01  X  0.00006  X  5000 ~T\^ 

(2500)2  X — —  -  ) 

200,000  X  2          J/ 

=  ([288,000,000  +  80,000,000] 

-7-  [2990  Vo. 000000003 2 7  +0.0469])^ 


/     368,000,000  f  o'l 

=  V  -  — —  =  41,400  feet  =  7.85  miles. 

V  0.169  +0.0469 

Thus,  the  economic  separation  of  converter  substations  on 
this  37.8-mile  electric  railway  is  7.85  miles;  consequently 


ANN  UAL  COSTS  IN 
THOUSANDS  OF  DOLLARS. 

CO  CO  CO  CO  0 

O  to  -f^  CD  a 

\ 

\ 

V 

\ 

x 

^ 

^ 

^^ 

,.  —  - 

—  - 

20 


30  40  50 

SPACING  IN  THOUSANDS  OF  FEET. 

Fig.  79- 


60 


5  substations  will  be  required,  each  equipped  with  two  con- 
version apparatus  units  of  250  K.W.  rated  capacity.  That 
7.85  miles  is  the  economic  distance  between  substations  is 
proved  by  computing  the  various  cost  items  for  the  railway 
which  depend  upon  this  distance  for  different  values  of  X, 
as  in  the  following  table,  and  as  shown  in  Fig.  79. 


188 


TRACTION  AND   TRANSMISSION. 


Cost  items. 

Substation  spacings  in  feet. 

20,000 

30,000 

41,400 

50,000 

60,000 

Wages,  Cw  

$14,400 
3,385 
18,558 

$9,600 

5,075 
17,685 

$6,960 
7,OOO 
17,440 

$5,760 
8,460 
I7,56o 

$4,800 
10,130 
17,765 

Copper,  Cc  
Equipment,  C8  .  .  .  . 

Total  

$36,343 

$32,350 

$31,400 

$31,780 

$32,695 

64.  Auxiliary  Storage  Batteries.  —  If  a  storage  battery 
in  series  with  a  compound- wound  booster1  be  connected 
between  the  positive  outgoing  and  negative  incoming  feeders 
of  a  substation,  the  two  may  be  so  adjusted  as  to  impress 
a  constant  voltage  upon  these  feeders.  As  a  result,  a  slight 
decrease  of  converter  voltage  under  abnormal  load  allows 
the  battery  to  discharge  into  the  distributing  system,  and 
also  a  slight  increase  of  converter  voltage  under  subnormal 
load  will  cause  the  battery  to  receive  a  charging  current 
from  the  converter.  The  use  of  a  battery,  therefore,  re- 
lieves the  substation  units,  the  transmission  line,  and  the 
power  station  apparatus  of  violent  instantaneous  fluctu- 
ations of  load.  If  the  battery  be  of  sufficient  capacity, 
it  may  also  serve  to  carry  the  peak  loads,  of  not  too  long 
duration,  which  are  common  on  interurban  systems.  If, 
again,  the  battery  be  of  very  large  capacity,  it  may  serve 
to  carry  the  characteristic  peak  loads  of  an  urban  system 
and  may  serve  to  supply  power  to  the  whole  system  in 
case  of  accident  in  the  power  station  or  on  the  transmission 
line.  The  use  of  a  battery,  therefore,  may  enable  one 
to  install  smaller  units  in  substations  and  in  generating 

1  For  a  discussion  on  the  connections  and  operation  of  boosters  and  stor- 
age batteries  see  Chapter  VIII,  Dynamo  Electric  Machinery,  Vol.  I,  by 
Sheldon  and  Hausmann. 


SUBSTATIONS.  189 

stations  and  to  operate  them  under  better  load  factors  and 
therefore  at  greater  efficiencies.  It  also  enables  one  to 
design  the  transmission  line  for  average  instead  of  maximum 
load  conditions.  The  saving  in  investment  for  station  equip- 
ments and  line  must  however  be  balanced  against  the  cost 
of  batteries  and  boosters,  and  the  decreased  energy  losses 
must  be  balanced  against  the  energy  losses  attendant  upon 
the  use  of  the  battery.  Furthermore,  the  cost  of  extra 
attendance  entailed  by  the  use  of  batteries  must  be  consid- 
ered. The  proper  capacity  of  such  a  battery  is  so  closely 
dependent  upon  the  characteristics  of  the  substation  load 
diagram  that  the  advisability  of  its  installation  can  be 
determined  only  from  the  study  of  the  specific  case. 

What  is  believed  to  be  the  largest  storage  battery  installa- 
tion in  the  world  is  that  which  is  used  in  connection  with 
the  electrical  zone  of  the  New  York  terminus  of  the  N.  Y.  C. 
&  H.  R:  R.  R.  The  complete  installation,  divided  into  eight 
groups,  is  capable  of  delivering  22,000  amperes  for  one 
hour,  which  is  sufficient  to  operate  the  whole  system,  under 
normal  conditions,  for  one  hour  in  case  of  failure  of  the 
generating  apparatus. 

65.  Arrangement  of  Apparatus.  —  The  arrangement  of 
apparatus  in  a  substation  is  governed  to  some  extent  by 
the  character  of  the  equipment  and  the  size  and  shape  of 
the  available  site.  It  is  desirable  to  have  all  apparatus 
on  one  floor;  but,  if  the  equipment  be  large,  the  switch 
gear  should  be  placed  on  a  gallery  so  that  the  attendant 
may  command  a  view  of  the  whole  station.  In  urban 
districts,  where  real  estate  is  expensive,  the  transformers, 
high-tension  switches,  and  lightning  arresters  are  often 
placed  on  a  second  floor.  Storage  batteries  when  used 
in  substations  are  usually  located  on  another  floor  or 


190 


TRACTION  AND   TRANSMISSION. 


SUBSTATIONS.  IQI 

in  a  separate  building  adjacent  to  the  main  substation. 
The  path  of  energy  from  the  transmission  line  to  the  dis- 
tributing feeders  should  be  as  short  and  direct  as  possible. 
This  leads  to  the  following  arrangement  across  the  station 


Fig.  8z. 

from  the  transmission  line:  high-tension  entrance  devices, 
lightning  arresters  and  switch  gear,  transformers,  reactances, 
converters,  low-tension  switch  gear,  and  outgoing  feeders. 
Fig.  80  is  a  sectional  view  of  a  substation  of  the  Milwaukee 
Electric  Railway  and  Light  Company.  This  substation 
has  a  rated  capacity  of  1200  K.W.  for  conversion  from 
66,000  volts  alternating  current  to  1200  volts  direct  current. 


192 


TRACTION  AND  TRANSMISSION. 


Fig.  82. 


Fig.  83. 


SUBSTATIONS. 


193 


Fig.  8 1  gives  a  view  of  the  low- tension  end  of  one  of  the 
substations  of  this  road,  the  reactances  surmounted  by 
starting  panels  being  shown  as  located  in  front  of  their 
respective  converters.  Fig.  82  shows  the  method  of  tapping 


Fig.  84. 

the  transmission  line  on  the  substation  roof,  and  shows  the 
high-tension  roof  bushings  for  insulating  the  supply  wires 
at  their  points  of  entrance  to  the  substation.  Figs.  83 
and  84  respectively  show  the  electrolytic  lightning  arresters 
and  the  high-tension  oil  switches  and  the  methods  em- 
ployed in  their  installation. 

66.   Portable    Substations.  —  On    most    electric    roads 
there  are  certain  sections  of  the  line  on  which  abnormally 


194  TRACTION  AND  TRANSMISSION. 

heavy  traffic  must  be  handled  at  infrequent  intervals  or 
only  during  a  certain  portion  of  the  year,  as  for  instance 
near  fairgrounds,  parks,  or  summer  resorts.  To  meet  such 
a  condition  and  to  guard  against  interruption  of  service 
due  to  accident  to  a  unit  in  any  substation,  it  is  much 
cheaper  to  make  use  of  portable  substations  than  to  in- 
stall permanent  spare  units.  These  substations  consist 
of  specially  arranged  cars  containing  complete  substation 
equipments,  of  the  converter  or  motor-generator  type, 
with  accessories.  The  standards  as  to  track  gauge,  height 
of  tunnels,  and  strengths  of  bridges  limit  their  character- 
istics to  500  K.W.,  60,000  volts,  and  1 50,000  pounds  weight. 
The  external  appearance  of  such  a  portable  substation  is 
shown  in  Fig.  85.  The  arrangement  of  apparatus  is  shown 
in  the  plan  and  elevation  of  Fig.  86,  and  Fig.  87  is  a  diagram 
of  the  circuit  connections.  The  positive  feeder  cable  is 
carried  to  a  terminal  block  on  the  outside  of  the  car  near 
the  roof,  for  convenient  connection  to  the  trolley  wire  or 
feeder.  The  incoming  high-tension  lines  may  be  connected 
directly  to  the  transmission  line;  but,  if  frequent  or  con- 
tinued use  of  the  portable  substation  in  one  locality  is 
necessary,  disconnecting  switches  should  be  mounted  on 
the  nearest  pole  to  facilitate  disconnecting  the  oil  switch 
without  having  to  cut  off  power  from  the  transmission 
line. 

The  use  of  such  portable  stations  insures  continuity  of 
supply  with  minimum  investment  in  permanent  substations, 
saves  large  investment  in  copper  and  equipment  on  lines 
infrequently  loaded,  provides  additional  capacity  at  any 
point  where  there  may  be  a  temporary  abnormally  heavy 
traffic,  and  may  furnish  power  for  extensions  during  the 
period  of  construction. 


SUBSTATIONS. 


195 


196 


TRACTION   AND   TRANSMISSION. 


SUBSTATIONS. 
PROBLEMS. 


197 


37.  Derive  an  expression  for  the  economic  spacing  of  substations,  the 
cross  section  of  the  composite  contact  conductor  being  prescribed  by  a 
mean  effective  drop  of  e  volts  at  a  point  midway  between  substations. 

Suggestion. — Obtain  an  expression  for  A  by  using  (3)  of  §  48,  insert  it  in 
(3)  and  (4)  of  §  62,  which  then  add,  multiply  by  L/\  and  use  in  place  of 
(6)  of  §  62  for  the  economic  determination. 


Fig.  87. 

38.  Assuming  the  same  wages  as  in  the  illustration  of  §  63,  what  influence 
would  a  change  of  the  hours  of  duty  to  eight  hours  a  day  have  upon  the 
spacing? 

39.  If  the  road  in  this  illustration  were  to  be  operated  with  single-phase 
currents  and  each  substation  were  to  be  equipped  with  two  single-phase 
transformers,  what  would  be  the  economic  spacing?     Use  cost  and  deficiency 
constants  given  in  §  62  and  neglect  reactance  drop  in  the  distributing  system, 

40.  If  all  the  equipment  in  all  the  substations  of  the  road  specified  in 


198  TRACTION  AND  TRANSMISSION. 

§  63  were  to  be  operated  for  8760  hours  per  year  at  rated  capacity,  what 
would  be  the  value  of  70  and  what  would  be  the  economic  spacing,  assuming 
1200  as  the  generator  voltage. 

41.  If  the  costs  of  switch  gear  and  lightning  arresters  for  each  substation 
on  the  road  specified  in  §  63  were  to  be  $2500  and  $3750  for  250  K.W.  and 
500  K.W.  capacities  respectively,  what  change  would  thereby  be  entailed 
in  the  cost  constants  /3'  and  gz  and  how  would  this  change  affect  the  value  of 
the  economic  spacing? 


TRANSMISSION  LINES.  199 


CHAPTER  IX. 

TRANSMISSION  LINES. 

67.  Location  of  the  Transmission  Line.  —  In  those  in- 
stallations which  employ  steam  or  internal-combustion 
prime  movers  in  the  power  station,  it  is  desirable  to  locate 
the  latter  with  reference  to  the  substations  which  it  supplies 
with  energy,  so  that  a  minimum  weight  of  conductor  mate- 
rial shall  be  required  and  the  drop  of  voltage  to  each  shall 
be  the  same.  This  location  is  termed  the  center  of  distribu- 
tion. Consider  two  substations  X  feet  apart  and  distant  Xi 
and  X2  feet  respectively  from  an  intermediate  power  station. 
Assume  the  substations  to  be  supplied,  over  a  three-phase 
line,  with  /i  and  72  annual  mean  effective  amperes  per  wire 
respectively.  If  the  specific  resistance  of  the  conductor 
material  be  p  ohms  per  circular  mil-foot,  and  the  respective 
cross  sections  be  A\  and  A2  circular  mils,  then  the 
power  lost  in  transmitting  energy  to  the  substations  is 
PI  =  3  pXi/i2/^4i  and  P2  =  3  pX2/22/^42  watts  respectively. 
If  the  weight  of  a  circular  mil-foot  be  w  pounds,  the  total 
weight  of  conductors  is 


W  =  3  w  (\iAi  -f-  X2^42)  pounds. 
Substituting  the  values  of  AI,  A^  and  X2  =  X  —  Xi, 

/Xi2/i2  ,   (X2-  2XXi  +  Xi2)/22\  ,  , 

W  =  9Pw(-y--+-  -j—         -J  pounds.       (i) 


200  TRACTION  AND  TRANSMISSION. 

For  a  minimum  weight  of  conductor  material,  the  differ- 
ential of  W  with  respect  to  \i  must  equal  zero.     Hence 


or 


If  the  drop  to  all  substations  be  the  same,  Pi/Ii  = 
and 

Xi/i  =  X2/2,  (3) 

wherein  \i  and  \2  now  represent  the  respective  distances  of 
the  substations  from  the  center  of  distribution.  For  any 
number  of  substations  located  at  various  points  along  a 
continuous  roadway  the  distance  of  the  center  of  distribu- 
tion from  any  point  is  X0  =  2X//Z/,  each  length  being 
measured  along  the  path  taken  by  the  transmission  line. 

The  location  of  the  power  station  at  the  center  of  dis- 
tribution is  subject  to  other  considerations,  such  as  the 
cost  of  real  estate,  future  growth,  facilities  for  the  receipt  of 
fuel  and  supplies  and  the  removal  of  ashes,  and  the  avail- 
ability of  water  for  condensing  purposes. 

In  the  case  of  hydraulic  installations,  the  location  of 
the  power  station  is  dependent  on  the  hydraulic  conditions; 
and  the  transmission  line  extends  from  it  to  the  nearest 
substation  or  to  the  one  nearest  the  center  of  distribution, 
whichever  may  prove  more  economical. 

Private  rights  of  way  for  the  transmission  line  are  to  be 
preferred  to  public  highways  and  generally  result  in  final 
economy  in  operation.  Rights  of  way  along  steam  rail- 
roads are  undesirable  because  of  insulation  troubles  likely 
to  result  from  coal  smoke.  It  is  not  practical  to  make  the 
right  of  way  so  wide  as  to  prevent  a  pole  or  tower  from 


TRANSMISSION  LINES.  2OI 

falling  on  the  abutting  property,  but  the  right  to  trim  trees 
on  both  sides  should  be  secured.  A  width  of  from  50  feet  to 
100  feet  is  ample. 

The  cost  of  right  of  way  amounts  to  from  25  to  50  per 
cent  of  the  total  cost  of  the  transmission  line.  All  con- 
tracts for  right  of  way  should  receive  careful  legal  attention. 

68.  Number  of  Phases.  —  The  proper  basis  for  deter- 
mining the  number  of  phases  to  be  employed  is  the  com- 
parison of  the.  weights  of  conductor  material  necessary  to 
transmit  the  same  power,  P  kilowatts,  over  the  same  dis- 
tance, S  feet,  with  the  same  loss,  Pf  watts,  and  the  same 
maximum  voltage,  E  kilovolts,  between  any  two  conductors. 
In  a  system  using  n  wires  each  of  cross  section  A  circular 
mils  and  carrying  /  amperes  the  loss  is 

watts.  (i) 

C*  7"2 

Therefore  A  =    p  f     circular  mils.  (2) 

The  total  weight  of  the  conductors  is  therefore 

W=  nwA  =  ^—7-  n2!2  pounds;  (3) 

that  is,  the  weight  is  proportional  to  the  square  of  the 
product  of  the  number  of  wires  by  the  current  flowing  in 
each  wire.  The  following  table  is  based  upon  the  current 
per  wire  in  amperes  for  transmitting,  at  unit  power  factor, 
one  kilowatt  with  a  loss  of  one  watt  per  foot  of  line  at  one 
effective  kilovolt  between  wires  of  greatest  potential  differ- 
ence. With  direct  currents  the  equivalent  voltage  is  V '2 
kilovolts.  For  the  three-wire  quarter-phase  system,  where 
the  center  conductor  carries  A/2  times  the  current  in  the 
outer  conductors,  it  is  assumed  that  the  cross  sections  of 


2O2 


TRACTION  AND   TRANSMISSION. 


the  conductors  will  be  so  chosen  that  the  loss  per  foot  is 
the  same,  P'/3,  in  each  conductor.  The  maximum  voltage 
between  any  two  conductors  is  assumed  the  same  in  all 
cases  because  its  value  determines  the  capacity  and  cost  of 
each  insulator.  The  center  wire  of  the  three-wire  quarter- 
phase  system,  however,  does  not  need  to  be  so  well  insu- 
lated as  the  outside  wires,  and  to  this  extent  the  above 
comparison  is  unfair  to  this  system.  Considering,  however, 
that  the  conductor  expense  considerably  exceeds  the  in- 
sulator expense  in  most  cases,  this  system  does  not  need  to 
be  considered  in  comparison  with  the  three-phase  system, 
which,  as  shown  in  the  table,  is  superior  to  all  systems  using 
alternating  currents. 

RELATIVE  WEIGHTS  OF   CONDUCTORS. 


System. 

Amperes  per  Wire. 

/'. 

„,, 

Relative 
Total 
Weight. 

Two  wires: 
Direct  current  

Single-phase  
Three  wires: 

I          P              ' 

i 
] 

\ 

i 

i 

3 

1, 
[ 

\ 

: 

2 

4 
3 

6 
4 

50 
100 

75 
150 

IOO 

\/2  E         -v/2 
P                  I 

Quarter-phase: 
Right-hand  wire  

Center  wire  

Left-hand  wire  

Four  wires: 
Quarter-phase  

7           P/2             ^2 

I        V~2      P/2            I 

P/2         '    V~2 

E/V~2            2 

r        P/2          I 
"      E      ~   2 

TRANSMISSION   LINES. 


203 


69.  Frequency.  —  The  Standardization  Rules  of  the 
A.  I.  E.  E.  give  25  and  60  as  standard  frequencies.  For 
transmission  lines  supplying  converting  substations  one  or 
the  other  should  be  used.  The  weights  and  costs  of  6o-cycle 


POUNDS  PER  K.W. 

—  ro  GO  -P>  01  c 
O  O  O  O  O  C 

\ 

N 

\ 

^ 

^ 

5^ 

^ 

—  -  — 

2 



JLES 

•               • 

1000  2000 

CAPACITY  IN  KILOWATTS. 
Fig.  88. 


3000 


transformers  are  less  than  those  for  25  cycles  and  the  oper- 
ating efficiencies  of  the  former  are  greater  than  those  of 
the  latter.  The  differences  are  not  very  great,  as  will  be 
seen  from  the  curves  in  Figs.  88  and  89,  which  refer  to 
1.00 


1000  2000 

CAPACITY  IN  KILOWATTS. 
Fig.  89. 


3000 


33,ooo-volt,  plain  steel,  air-blast  transformers.  Induction 
motors  for  higher  frequencies  are  also  cheaper,  but  operate 
at  lower  power  factors.  At  the  lower  frequency  it  is  less 
difficult  to  operate  generators  and  other  synchronous  appa- 


204  TRACTION  AND  TRANSMISSION. 

ratus  in  parallel,  because  the  unavoidable  variations  in  speed 
are  smaller  in  proportion  to  the,  angular  velocity.  The 
charging  current  of  the  line  and  the  inductive  drop  are  less 
with  low  frequencies,  and  may  give  a  better  regulation. 
For  lines  of  moderate  length  it  might  prove  desirable  to 
use  60  cycles,  but  the  general  tendency  is  to  use  25  cycles. 
For  lines  of  great  length,  however,  it  is  usually  undesir- 
able to  use  60  cycles  for  the  following  reasons.  In  all  large 
systems  odd  harmonic  frequencies  of  voltage  and  current,  of 
which  the  third  and  fifth  may  predominate,  are  likely  to  be 
present  and  be  superposed  upon  the  fundamental  frequency. 
Electromotive-force  harmonics  may  be  due  to  armature 
reaction,  to  pulsation  of  inductance,  to  the  distribution  of 
armature  windings,  or  to  non-uniform  distribution  of  mag- 
netic flux  in  the  air  gaps  of  the  generators.  Current  har- 
monics may  result  from  similar  causes  associated  with  the 
structures  forming  the  receiving  apparatus.  Every  trans- 
mission line,  because  of  its  inductance  and  capacity,  has  a 
resonant  frequency.  The  magnetic  field  of  the  former  and 
the  electric  field  of  the  latter  serve  for  the  storage  of  energy 
in  kinetic  and  potential  forms  respectively.  Such  capacities 
for  the  storage  of  the  two  forms  of  energy  are  characteristic 
of  every  medium  for  wave  propagation,  and  their  magni- 
tudes determine  the  velocity  of  the  propagation.  As  will 
be  shown  later,  the  velocity  with  which  an  impressed  differ- 
ence of  potential  travels  away  from  a  generator  along  a  line 
of  usual  construction  is  but  slightly  less  than  the  velocity 
of  light,  that  is,  in  the  neighborhood  of  186,000  miles  per 
second.  Now  a  transmission  line  with  both  ends  open  or 
both  ends  short-circuited  has  a  resonant  frequency  which 
corresponds  to  a  wave  length  equal  to  twice  the  length  of 
the  line,  as  is  the  case  with  an  organ  pipe  open  at  both  ends. 


TRANSMISSION  LINES.  205 

On  the  other  hand  its  length  is  but  a  quarter  wave  length 
when  one  end  is  open  and  the  other  short-circuited,  as  is 
the  case  with  a  closed  organ  pipe.  In  the  latter  condition 
a  line  155  miles  long  would  correspond  to  a  wave  length  of 
4  X  155  =  620  miles  and  the  corresponding  resonant  fre- 
quency would  be  186,000  miles  per  second  divided  by  620 
miles,  or  300  per  second,  which  is  the  frequency  of  the  fifth 
harmonic,  when  the  fundamental  is  60  cycles  per  second. 
The  use  of  '60  cycles  on  a  line  of  such  length  is  therefore 
likely  to  result  in  resonant  oscillations  of  current  and  electro- 
motive force  which  may  prove  disastrous. 

For  the  operation  of  single-phase  railroads  a  frequency  of 
less  than  twenty-five  permits  of  a  marked  reduction  in  the 
size  of  a  motor  for  a  given  output;  and  yet  almost  all  such 
roads  have  adopted  25  cycles.  The  New  York,  New  Haven 
&  Hartford  Railroad  is  an  instance.  The  Midi  Railway 
of  France,  among  others,  has  adopted  15  cycles.  A  deter- 
mination of  the  most  suitable  frequency  for  such  installations 
is  desirable,  involves  extensive  knowledge  as  to  costs  and 
peculiarities  in  operation,  and  must  be  considered  as  to  its 
bearing  on  the  general  question  of  the  standardization  of 
practice. 

70.  Economic  Voltage.  —  The  economic  voltage  between 
the  wires  of  a  transmission  line  depends  upon  the  amount 
of  power  and  the  distance  over  which  it  is  to  be  transmitted 
as  well  as  upon  the  various  cost  factors  of  equipment  and 
energy.  To  understand  the  method  for  its  determination 
and  to  avoid  complexity,  assume  a  single  three-phase  line 
of  equivalent  length  5  feet  supplying  at  a  maximum  P  kilo- 
watts, divided  equally  among  n  substations,  each  of  which 
contains  two  ponverter  units  of  rated,  capacity  P/2  n  kilo- 
watts. Assume  further  that  the  rated  capacity  of  each  of 


206  TRACTION  AND   TRANSMISSION. 

the  three  single-phase  step-up  transformers  at  the  power 
station  is  P/$  kilowatts. 

Conductor  Expense.  —  If  the  yearly  mean  effective  power 
factor  be  cos  0  and  the  voltage  between  wires  be  E  kilovolts, 
the  full  load  current  per  wire  will  be 

/  =  -  amperes. 

v  3  E  cos  0 

If  the  resistance  of  a  mil-foot  of  conductor  be  p  ohms,  the 
resistance  of  each  wire  will  be  pS/A  ohms;  and  if  the 
equivalent  effective  yearly  hours  of  operation  on  full  load 
current  be  h,  the  annual  loss  of  energy  in  all  three  wires 
will  be 

$RPh  phSP2 


1000        1000  AE2  cos2  <f> 


,  .. 

kilowatt  hours. 


If  the  mean  annual  cost  of  delivering  a  kilowatt  hour  to  the 
middle  of  the  line  be  cs  dollars,  the  annual  expense  for 
energy  lost  in  the  line  conductors  will  be 


n  ,  z  f  N 

Cc   =  -    -^j—  -  -  —  dollars.  (i) 

22 


1000 


If  w  be  the  weight  of  a  mil-foot  in  pounds,  c2  be  the  cost 
per  pound,  and  p%  be  the  rate  of  interest  and  depreciation 
on  the  cost  of  conductors,  the  annual  charge  on  the  capital 
outlay  for  all  three  conductors  is 

Cc"  =  3  pzC^wSA  dollars.  (2) 

Since  equations  (i)  and  (2)  must  be  equal  to  each  other  for 
a  minimum  annual  cost,  they  may  be  equated  and  solved 
for  A,  giving 


A  =  — ~  V  ~  -^ circular  mils.  (3) 

E  cos  0  V    000    2C2W 


TRANSMISSION   LINES.  207 

Substituting  this  value  of  A  in  (2)  and  multiplying  by  2 
so  as  to  include  (i),  the  total  annual  charge  against  the 
conductors  will  be 


Cc  =  Cc'+  C>  =   ai09         VclMM^  i  dollars'     (4) 

L       COS  <j>  itL 

and  representing  the  bracketed  expression  by  Kc, 

Cc  =  KJE  dollars.  (5) 

Pole  and  Insulator  Expense.  —  There  is  as  yet  no  stand- 
ard form  of  construction  of  towers  or  poles.  Many  rigid 
steel  towers  have  been  installed  and  recently  flexible  steel 
structures  costing  materially  less  than  those  of  the  rigid 
type  have  been  used  with  success.  The  determination  of 
the  type  to  be  employed  can  best  be  made  in  connection 
with  a  specific  problem,  which  determination  will  also  give 
the  economic  distance,  X'  feet,  between  poles.  With  poles 
of  the  flexible  type  the  cost,  cp,  does  not  materially  vary 
with  the  voltage  between  the  line  wires.  Furthermore, 
if  insulators  of  the  suspension  type  be  employed,  the 
cost  of  each  one  per  kilovolt,  ct,  is  practically  constant. 
Since  the  number  of  poles  to  be  used  on  a  line  of  real  length 
S'  equals  S'/\'  and  the  number  of  insulators  is  three  times 
this,  if  the  annual  interest  and  depreciation  on  these  items 
be  pp  and  pi  respectively,  the  annual  pole  and  insulator 
expense  is 

CP  =  [pPcpS7\f]  +  [3  PiCiS'/\'}  E  dollars,  (6) 

and,  representing  the  bracketed  expressions  by  Kp  and  Kp 
respectively, 

Cp  =  Kp  +  KP'E   dollars.  (7) 

Pin-type  insulators  cost  more  per  kilovolt  as  the  oper- 
ating voltage  increases.  It  is  assumed  by  some  that  the 
cost  thereof  increases  as  the  cube  of  the  voltage. 


208  TRACTION  AND   TRANSMISSION. 

Transformer  Expense.  The  costs  of  transformers  depend 
not  only  upon  their  rated  capacity  but  also  upon  the  volt- 
age at  the  high-tension  terminals.  The  insulation  expense 
increases  with  voltage.  For  the  same  capacity  and  voltage 
water-cooled  transformers  are  cheaper  than  air-cooled  ones. 
Power-station  facilities  are  generally  such  as  to  permit  the 
use  of  water-cooled  step-up  transformers,  while  air-blast 
transformers  are  common  in  substations.  A  study  of  the 
prices  for  transformers  shows  that  the  cost  of  each,  ctj  can 
be  expressed  by  the  following  formula,  where  E  represents 
the  high-tension  kilovoltage,  PI  the  rated  capacity  in  kilo- 
watts, and  K  and  K'  are  constants  : 

ct  =  (KE  +  K')  VP1  dollars.  (8) 

This  formula  applied  to  transformers  where  PI  varies  from 
500  to  4000  and  E  from  22  to  66,  gives  results  within  the 
variations  between  the  quotations  from  different  manufac- 
turing companies.  It  is  approximately  true  also  for  higher 
voltages.  In  a  particular  problem  with  many  substations 
it  would  be  wise  to  make  use  of  two  sets  of  values  for 
the  constants  applying  respectively  to  the  power  and  sub- 
station transformers. 

The  number  of  transformers  in  the  power  station  is 
three;  each  of  capacity  P/$  kilowatts.  There  are  6  n  in 
the  n  substations;  each  of  capacity  P/6  n  kilowatts.  If 
pt  be  the  rate  of  interest  and  depreciation  on  this  apparatus, 
the  annual  expense  for  transformers  in  dollars  is 


Ct  =  3  Pt  (KE  +  K')  Vl^/3  +  6  ptn  (KE  +  K')  Vp/6n, 
which  by  combining  and  transposing  becomes 


(9) 


TRANSMISSION  LINES.  209 

and,  if  Kt  and  Ktf  represent  the  bracketed  expressions,  the 
annual  transformer  expense  may  be  represented  as 

Ct  =  Kt  +  K/E  dollars.  (10) 

Auxiliary  Expense.  —  The  costs  of  aluminum  lightning 
arresters,  choke  coils,  and  oil  switches  increase  with  the 
voltage  of  the  circuits  with  which  they  are  to  be  connected. 
The  first  mentioned  increase  more  rapidly  than  the  voltage, 
the  second  nearly  directly,  and  the  last  less  rapidly.  If 
their  combined  costs  for  different  voltages  be  determined, 
it  will  be  found  that  the  cost  per  three-phase  unit  may  be 
expressed,  with  sufficient  accuracy,  as  a  linear  function  of 
the  voltage.  Considering  a  unit  to  consist  of  a  four-tank 
arrester,  three  choke  coils,  and  a  triple-pole  oil  switch,  and 
one  unit  to  be  installed  in  each  substation  and  in  the  power 
station,  if  ca  be  the  cost  per  unit  per  kilo  volt  and  pa  be  the 
rate  of  interest  and  depreciation,  the  annual  expense  charge- 
able to  these  auxiliaries  will  be 

Ca  =  [paca(n  +  i)]E,  (n) 

and  representing  the  bracketed  expression  by  Ka, 

Ca  =  KaE  dollars.  (12) 

Solution.  The  economic  voltage  is  now  determined  by 
adding  the  expressions  for  the  annual  expenses  for  con- 
ductors, poles,  insulators,  transformers,  and  auxiliaries, 
differentiating  the  sum  with  respect  to  E,  equating  to  zero 
and  then  solving  for  E  as  follows: 

c  =  cc  +  cp  +  ct  +  ca, 

C  =  (Kp  +  Kt)  +  KC/E  +  (Kpf  +  Kt'+  Ka)E  dollars,   (13) 
(K,f  +  K!  +  K.)  =  o. 


210  TRACTION  AND  TRANSMISSION. 

Therefore  the  economic  voltage  between  wires  is 


Substituting  the  values  of  the  constants  from  equations 
(4),  (6),  (9),  and  (u), 

,-,  _        _  (0.1096  PS  '/cos,  0)  V 

" 


paca  (n  +  i) 
kilovolts,  (15) 

and  the  economic  cross  section  of  the  conductors  is  found 
by  inserting  this  value  in  equation  (3). 

In  the  above  derivation  the  total  transformer  capacity 
at  the  power  station  has  been  assumed  equal  to  that  in  all 
substations.  In  existing  plants  the  latter  exceeds  the 
former  by  from  40  per  cent  to  60  per  cent.  This  is  feasible 
when  the  load  peaks  of  the  different  substations  are  not 
simultaneous.  The  ratio  of  the  maximum  load  supplied  at 
one  time  to  all  substations  to  the  sum  of  the  maximum  loads 
on  each  substation  is  termed  the  diversity  factor.  Further- 
more, it  has  been  assumed  that  the  power  factor  at  maxi- 
mum load  is  unity.  This  can  be  realized  as  resulting  from 
the  phase  of  the  currents  taken  by  converters  at  maximum 
load  when  the  voltage  regulation  is  that  produced  by 
reactances.  The  converters  then  tend  to  correct  the  power 
factor  of  the  line.  The  energy  given  to  the  line  at  the 
power  station  must,  however,  exceed  that  which  is  deliv- 
ered to  the  substations  by  the  amount  which  is  lost  in  the 
transmission  line. 

Generally  a  transmission  line  extends  from  the  power 
station  to  one  of  several  substations,  then  divides,  and  con- 
tinues to  the  other  substations.  The  currents  in  the  branch 


TRANSMISSION  LINES.  211 

conductors  are  less  than  in  the  conductors  of  the  main 
line  and  the  cross  section  is  accordingly  reduced.  The  eco- 
nomic cross  section  of  a  conductor  of  a  branch,  of  length  SB 
feet  between  substations,  is  determined  by  equation  (3) 
and  the  total  annual  charge  against  the  conductors  by 
equation  (4) .  If  the  mean  annual  effective  power  factor  on 
the  branch  be  the  same  as  on  the  main  line,  then  the  main 
line  may  be  considered  as  having  added  to  it  a  length  SE 
such  that  the.  annual  conductor  expense  for  the  branch  is 
included  in  that  for  the  main  line.  Remembering  that 
/  =  -P/v7^  E  cos  0,  and  equating  two  expressions  like  equa- 
tion (4) ,  applied  to  lengths  SB  and  SE  and  to  currents  IB  and 
/  respectively, 

IBSB  =  ISa, 

whence  SE  =  SB!B/I-  (16) 

If  the  distance  from  the  power  station  to  the  first  sub- 
station be  So  feet,  then  the  equivalent  length  to  be  used  in 
calculating  the  annual  expense  of  conductors  is 

5  =  So  +  2SE,  (17) 

the  last  term  including  the  extension  of  length  due  to  all 
branches. 

In  calculating  the  annual  expense  against  insulators  and 
poles,  however,  the  real  length  of  the  complete  line  must  be 
taken. 

71.  Numerical  Illustration.  —  Assume  a  single  three- 
phase  2 5 -cycle  line  having  an  equivalent  length  of  61  = 
350,000  feet  and  a  real  length  of  S'  =  450,000  feet,  trans- 
mitting, at  maximum  rated  load,  P  =  3000  kilowatts 
divided  equally  among  n  =  5  substations  at  the  receiving 
end  of  the  line.  Let  the  annual  effective  power  factor  be 
cos  $  =  0.90,  the  equivalent  annual  hours  of  operation  be 


212  TRACTION   AND   TRANSMISSION. 

h  =  3500,  and  let  the  constants  have  the  following  values 
—  the  bracketed  values  being  suggestive  of  the  proper  order 
of  magnitude : 

P  =  10.  cp  =  [80]. 

w  =  0.00000303.  X'  =  [600]. 

p2  =  [O.06].  Ci    =   [O.2O]. 

c2  =  [o.i8].  K  =  [0.50]. 

cz  =  [o.oi].  K'  =  [65]. 

Pi  =  PP   =  Pt   =  Pa  =   [0.12].  Ca     =   [SO]. 

Substituting  these  values, 

Kc  =  (0.1096  X  3000  X  350,000/0.9), 

V.oi  X  10  X  3500  X  .06  X  .18  X  0.00000303  =  432,000, 
KP'=  3  X  0.12  X  0.2  X  450,000/600  =  54, 
Kt'  =  3  X  0.12  Xo.5  Viooo  (i  +  Vio)  =  23.75, 
Ka  =  0.12  X  50  X  6  =  36. 

Substituting  these  values  in  equation  (14),  the  economic 
voltage  is 


-     432'°°0      -  =  61.7  kilovolts. 
54  +  23.75  +  36 

The  American  Institute  of  Electrical  Engineers  recom- 
mends as  standard  voltages  for  transmission  circuits  6.6, 
n,  22,  33,  44,  66,  or  88  kilovolts.  Furthermore,  55-kilo- 
volt  apparatus  is  listed  by  manufacturers.  The  problem 
in  hand  requires  for  greatest  economy  61.7  kilovolts,  a 
value  which  falls  between  two  of  those  recommended. 
It  is  instructive  to  find  what  additional  annual  expense 
would  be  entailed  in  following  the  recommendations.  The 
annual  expense  items  for  different  voltages  are  therefore 
given  in  the  following  table. 


TRANSMISSION  LINES. 
ANNUAL  EXPENSES  AT  DIFFERENT  VOLTAGES. 


213 


Items  of  Annual  Expense. 

Kilovolts  between  Wires. 

44 

55 

61.7 

66 

Conductors: 
Kc/E                           

9,810 

7,200 
2,378 

4,050 
1,044 

1,582 

7,860 

7,2OO 
2,970 

4,050 
1,314 

1,980 

7,010 

7,200 
3,33° 

4,050 
1,467 

2,220 

6,550 
7,200 

3,560 
4,050 

1,568 

2,376 

Poles  and  insulators: 
KP  

Kp'E  

Transformers: 
Kt  
Kt'E 

Auxiliaries: 

KaE 

Total  annual  expense  

$25,094 

$24,404 

$24,307 

$24,334 

These  results  show  that  the  additional  annual  expense 
would  be  but  $97  at  55  kilo  volts  or  $27  at  66  kilo  volts,  and 
therefore  the  latter  voltage  should  be  adopted.  The  use 
of  the  higher  voltage  also  requires  a  somewhat  smaller 
initial  investment.  It  may  be  desirable  in  some  cases 
materially  to  increase  the  operating  voltage  above  that 
determined  in  this  manner,  in  order  to  limit  the  first  cost. 

72.  Separation  of  Conductors.  —  The  separation  of  con- 
ductors at  the  insulators  must  be  sufficient  so  that,  at  the 
middle  of  the  spans,  the  conductors  may  not  swing  so 
closely  together  as  to  occasion  a  discharge  between  them. 
A  limitation  to  the  future  further  increase  of  voltage  be- 
tween conductors  is  presented  by  the  insulating  properties 
of  the  atmosphere.  If  the  voltage  between  two  aerial 
conductors  be  gradually  increased  a  critical  voltage  is  reached 
at  which  a  discharge  of  electricity  from  the  conductors  into 
the  air  is  initiated.  This  critical  voltage  depends  upon  the 
sizes  of  the  conductors  and  the  distance  between  them, 
and  upon  the  temperature  and  pressure  of  the  air.  The 


214  TRACTION  AND  TRANSMISSION. 

conductors  when  seen  at  night  are  surrounded  by  a  lumi- 
nous envelope  of  red- violet  color.  The  phenomenon  is 
termed  corona.  At  normal  pressure  and  temperature,  the 
air  breaks  down  and  becomes  convectively  conductive  when 
subjected  to  a  uniform  electric  field  strength  of  76  effective 
kilovolts  per  inch  or  30  effective  kilovolts  per  centimeter. 
The  critical  condition  is  determined  by  the  maximum  instan- 
taneous voltage  gradient,  and  therefore  the  critical  voltage 
for  direct  currents  is  V2  times  the  above  value,  or  107  kilo- 
volts  per  inch.  These  values  do  not  apply  when  the  dis- 
tances between  the  charged  conductors,  which  occasion  the 
electric  field,  are  smaller  than  half  an  inch,  as  will  be  shown 
later.  The  electric  fields  in  the  vicinity  of  the  conductors 
of  an  ordinary  aerial  line  are  not  uniform,  for  the  lines  of 
electrostatic  flux  diverge  in  leaving  the  conductors.  The 
amount  of  divergence  depends  upon  the  sizes  of  the  con- 
ductors and  the  distance  between  them.  These  factors  and 
the  value  of  the  critical  voltage  between  conductors  are 
involved  in  the  expression  for  the  critical  electric  field  in- 
tensity at  the  surface  of  the  conductor,  and  therefore  the 
electrical  conditions  for  the  starting  of  corona  may  be  de- 
termined from  the  critical  field  intensity  at  the  surface  of 
the  conductor.  Curve  I  of  Fig.  90,  given  by  Ryan  and 
based  upon  experiment,  shows  the  relation  which  exists 
between  critical  surface  intensity  in  effective  kilovolts  per 
inch  and  conductor  diameters.  Curve  II  of  this  figure 
gives  the  critical  effective  voltages  between  cylindrical  con- 
ductors mounted  coaxially  within  a  hollow  cylinder  having 
an  internal  diameter  of  fifteen  inches.  It  therefore  follows 
that  the  corona  envelope  which  surrounds  the  conductor 
is  a  region  in  which  the  air  is  made  conducting  because  it 
is  subjected  to  an  electric  field  intensity  of  greater  value 


TRANSMISSION   LINES. 


215 


than  76  effective  kilo  volts  per  inch.  The  outside  terminus 
of  its  radius  is  the  equipotential  surface  having  this  critical 
value. 

The  physical  process  underlying  the  initiation  of  corona 
is  termed  ionization  by  collision.  Due  primarily  to  the 
presence  of  radioactive  substances  on  the  earth,  there  are 


iiDU 

I 

\ 

I  oon 

\ 

\ 

o 

z 

\ 

II 

70 

Vr' 

01 

"^ 

^ 

111 

\- 

J>, 

v|0^ 

-^ 

^v' 

j— 

Q. 

V 

^ 

^ 

! 

<\ 

o 

_J 

o 

\ 

/ 

^v> 

^ 

\> 

i^ 

o 

_J 

^x 

^^ 

Id 

/ 

^/ 

> 

< 

'/ 

•  —  — 

^-  —  , 

-rr-T 



*>* 

Z 

10  eo 

50 

Q 

.1         .2        .3        .4        .5        .6 
DIAMETER  IN   INCHES 
Fig.  90. 


.7       .8  ^ 


always  present  in  the  atmosphere  positive  and  negative 
ions,  each  carrying  a  charge  of  4.9  X  io~10  abstat  coulombs 
or  multiples  thereof.  Under  ordinary  conditions  the  num- 
ber present  per  cubic  centimeter  is  of  the  order  of  1000, 
and  this  number  is  inadequate  to  permit  of  appreciable 
convective  conduction  by  the  air  of  the  problem  under 
consideration.  Each  of  these  ions  however,  if  subjected  to 
an  electric  field  intensity  of  sufficient  magnitude,  will  acquire 
adequate  kinetic  energy  in  traversing  a  free  path,  to  ionize 
a  neutral  air  molecule  with  which  it  collides.  The  energy 
required  to  ionize  a  gas  particle,  as  determined  by  various 


216 


TRACTION  AND   TRANSMISSION. 


a 


methods,  is  of  the  order  4  X  10  u  ergs.  Since  the  free 
path  of  a  gas  particle  increases  directly  with  decrease 
of  pressure  at  constant  temperature  and  with  increase  of 
temperature  at  constant  pressure,  the  value  of  the  critical 
voltage  will  accordingly  decrease  with  like  proportionality. 
One  characteristic  of  corona,  a  perfectly  satisfactory 
physical  basis  of  which  has  not  as  yet  been  given,  is  that 
to  start  it  around  a  conductor  of  given  diameter  a  specific 
radial  thickness  of  envelope  is  essential.  The  critical  field 

intensity,  if  produced  in- 
side the  ultimate  en- 
velope, will  not  initiate 
the  phenomenon.  Ryan 
has  termed  this  thickness 
the  striking  distance  and 
gives  its  value  for  con- 
ductors of  various  diam- 
o  .1  .2  .3  .4 

DIAMETER  OF  CONDUCTOR,  INCHES,  eters    in    the   form  of   a 

Fig>91*  curve  as  in  Fig.  91.     For 

conductors  of  "very  great  diameter  "  however  he  gives 
the  "value  of  about  0.25  inch."  To  initiate  corona  be- 
tween conductors  separated  by  a  distance  less  than  the 
sum  of  their  respective  striking  distances  requires  a  greater 
field  intensity  than  if  they  were  further  separated. 

The  critical  voltage  at  which  power  loss  begins  through 
the  atmosphere  between  two  clean  power-transmission  con- 
ductors of  D  inches  diameter  and  spaced  d  inches  apart 
interaxially  may  be  expressed  by  the  following  equation 
which  embodies  the  researches  of  Ryan,  Whitehead  and 
Watson: 


.07 
.06 
.05 
.04 
.03 
.02 
01 

^ 

.  

_       - 

—  —  • 

/ 

/ 

/ 

CRITICAL  CORONA 
STRIKING  DISTANCES 

/ 

/ 

Em  =  47.8  D0-8  log«-    kilovolts 


(i) 


TRANSMISSION   LINES. 


217 


at  20  degrees  centigrade  and  760  mm.  pressure,  for  wire 
sizes  between  No.  16  and  No.  oooo;  where  Em  is  the  maxi- 
mum value  of  the  voltage  on  a  representative  single-wire 


200 


1SO 


0.2  0.3  0.4 

CONDUCTOR  DIAMETER   (INCHES) 

Fig.  92. 


0.5 


perfectly  conducting  earth-return  circuit,  or  voltage  to 
neutral.  The  critical  voltage  for  conductors  of  given  size 
and  spacing  is  practically  independent  of  conductor  mate- 
rial, and  also  of  the  velocity  and  humidity  of  the  air.  As 


2l8  TRACTION  AND  TRANSMISSION. 

has  been  shown,  this  critical  voltage  varies  almost  exactly 
with  the  density  of  the  air.  Thus,  to  render  equation  (i) 
applicable  to  lines  under  all  atmospheric  conditions,  the 
following  factor  must  be  inserted  therein: 

d=J_  .  273  +  20  =  0.385  p^  (a) 

760        273  +  t        273  +  / 

where  p  is  the  pressure  in  millimeters  of  mercury  and  /  is 
the  temperature  in  degrees  centigrade.  Consequently  in 
higher  altitudes  and  at  high  temperatures  the  critical  volt- 
age will  be  lower. 

The  critical  voltages  between  conductors  on  three-phase 
circuits  are  shown  graphically  in  Fig.  92  by  curves  plotted 
from  equation  (i).  The  effective  voltage  values  correspond- 
ing to  the  appearance  of  corona  are  given  for  conductors 
from  No.  10  to  No.  oooo  B.  &  S.  with  various  spacings  at  a 
temperature  of  20  degrees  centigrade  and  760  mm.  pressure. 

The  foregoing  expressions  dictate  the  separation  of  aerial 
conductors  for  a  given  operating  voltage,  the  size  of  wire 
having  been  determined  by  the  energy  transmitted  and 
from  economic  considerations.  Let  the  numerical  constant 
of  equation  (i),  the  atmospheric  density,  the  crest  factor 
(or  ratio  of  maximum  voltage  to  effective  value),  the  ex- 
tension factor  for  multiphase  circuits,  and  the  factor  of 
safety  (or  ratio  of  critical  voltage  to  impressed  voltage),  be 
embodied  in  a  single  coefficient  K.  Then  solving  the  ex- 
pression for  d,  there  results  the  necessary  separation  between 
conductors  for  the  avoidance  of  corona  as 

E 

D     *W 

a  =  — e 

12 

d = T2  (cosh     + sinh      feet 


TRANSMISSION  LINES. 


219 


where  E  is  the  effective  voltage  between  conductors  in 
kilo  volts. 

As  an  illustration,  let  it  be  required  to  determine  the 
proper  distance  between  No.  oooo  stranded  conductors 
(0.53  inch  diameter)  of  a  i4o,ooo-volt  three-phase  trans- 
mission line  in  a  locality  where  the  highest  temperature  is 


100 
80 

40 
30 

20 
10 
5 

s 

/ 

y 

/ 

. 

7 

/ 

/ 

y 

/ 

/ 

/ 

' 

/ 

7 

140,000  VOLT,  3  PHASE 
LINE  WITH  0.53  IN. 
CONDUCTORS. 

1.2  1.3 

FACTOR  OF  SAFETY. 

Fig  93- 


1.4 


1.5 


35  degrees  centigrade  and  the  lowest  atmospheric  pressure 
is  600  mm.  Assuming  a  harmonic  impressed  electromo- 
tive force,  and  a  factor  of  safety  of  i.i,  the  value  of  K  is 

0.385  X  600        i       -        ! 
I'Q-~  —  X — 7=vi  X  — 

273  +  35        V2     ^      i.i 


K 


39-9» 


220  TRACTION  AND  TRANSMISSION. 

and 

R      =          140  o 

KD08      39.9X0.602       5>  3> 

consequently  the  distance  between  the  conductors  when 
triangularly  spaced  is 


d  =          X  340.359  =  15-°  feet. 

To  realize  a  larger  factor  of  safety  than  i.i  as  above,  a 
much  greater  separation  of  the  line  wires  is  necessary. 
The  influence  of  the  factor  of  safety  upon  the  corresponding 
distance  between  conductors  of  the  line  just  cited  is  shown 
by  the  curve  plotted  with  semi-logarithmic  coordinates  in 
Fig.  93,  all  other  conditions  remaining  unchanged. 

73.  Resistance  of  Conductors.  —  The  resistance  per  mile 
of  length  of  a  conductor  in  which  the  current  density  is 
uniform  throughout  the  cross  section,  A  circular  mils,  at 
any  temperature  /  degrees  centigrade  is 


where  p  is  the  resistivity  in  ohms  per  circular  mil-foot  at 
o  degrees  centigrade,  and  a  is  the  mean  temperature 
coefficient  of  electrical  resistance;  accepted  values  of  which 
for  the  usual  line  materials  being 

pa  w 

Copper  (hard  drawn)  9.54     0.00415      0.00000303 

Aluminum  (hard  drawn)      15.8       0.0039       0.00000091 

The  weights  per  circular  mil-foot  in  pounds  of  copper  and 
aluminum  are  given  in  the  last  column. 

Uniform  distribution  of  current  in  conductors  is  realized 
in  the  transmission  of  continuous  currents.     In  conductors 


TRANSMISSION   LINES. 


221 


carrying  alternating  currents,  the  current  density  at  the 
surface  is  greater  than  at  the  axis  of  the  conductors;  this 
unequal  distribution  of  current  increases  with  the  fre- 
quency of  the  impressed  electromotive  force  and  manifests 
itself  as  an  increase  in  resistance  by  rendering  part  of  the 
conductor  cross  section  ineffective.  Fig.  94  shows  the  per- 


PERCENTAGE  RESISTANCE  INCREASE 

-*  to  CO 
-0000 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

^r 

^ 

/ 

-- 

^^ 

0               1.5               2.0 

2. 
Fig. 

5 

z 

94- 

3. 

0 

3. 

5 

4.0 

centage  increase  of  resistance  of  conductors  when  traversed 
by  alternating  currents  over  that  when  traversed  by  contin- 
uous currents  in  terms  of  a  function  z,  which  is  denned  as 


z  —  r 


where  r  is  the  radius  of  the  wire  in  inches  and/  is  the  fre- 
quency in  cycles  per  second. 

The  resistances  per  unit  length  of  cables  are  somewhat 
greater  than  those  of  solid  conductors  of  like  cross-sectional 
areas.  If  there  be  N  strands  in  a  cable  having  a  lay  of  i 
in  n  (i.e.,  the  pitch  of  the  strand  helices  is  n  times  their 
diameter  measured  along  the  central  wire),  the  total  re- 


222 


TRACTION  AND   TRANSMISSION. 


sistance  of  the  cable,  assuming  no  current  flow  between 
strands,  will  be 

N 


Thus,  the  resistance  of  a  ig-strand  cable  having  a  lay  of  i  in 
15  is  2.05  per  cent  greater  than  the  resistance  of  a  solid 
conductor  of  equal  cross-sectional  area. 

74.  Line  Inductance. —  Conductors  carrying  a  varying 
current  are  surrounded  by  a  magnetic  field  of  varying  in- 
tensity. A  change  in  the  magnetic  flux  which  encircles  a 
conductor  develops  in  it  an  electromotive  force  of  self- 
induction.  If  the  conductors  carry  an  alternating  current 
an  alternating  electromotive  force  will  be  induced  in  them, 
the  magnitude  of  which  depends  upon  the  time  rate  of 

7  Jf 

change  of  current,  that  is,  its  value  at  the  instant  /  is  L  — , 

dt 

where  L  represents  the  inductance  of  the  circuit  and  /'  is 
the  instantaneous  current  value. 


Fig.  95- 


To  determine  the  inductance  L  per  unit  length  of  single 
wire,  consider  a  two- wire  line  carrying  an  alternating  cur- 
rent, the  conductors  being  of  radius  r  and  separated  be- 
tween centers  by  a  distance  d,  as  shown  in  Fig.  95.  The 


TRANSMISSION   LINES.  223 

magnetic  flux  which  passes  through  an  element  outside  of 
the  conductor  of  width  dx  and  of  unit  axial  length  is  equal 
to  the  magnetomotive  force  divided  by  the  reluctance,  or 

•,,        4  *i         -  dx 
d$!  =  — —  =  2  i  —  > 

2  irX  X 

dx 

where  i  is  the  instantaneous  value  of  the  current  flowing  in 
the  conductors.  The  total  magnetic  flux  which  passes  be- 
tween the  wires  due  to  the  current  in  one  of  them  is  obtained 
by  integration  for  values  of  x  between  d  —  r  and  r,  as 

d-r 


.Cd~rdx 

=   2  £   I  —  = 

Jr        oc 


21 


r 
d  and  r  being  both  expressed  in  terms  of  the  same  unit. 

The  magnetic  flux  which  passes  through  the  conductor 
material  is  of  appreciable  magnitude  owing  to  the  greater 
flux  density  near  the  wires.  Assuming  for  simplicity  that 
the  current  is  uniformly  distributed  over  the  cross  sections 
of  the  cylindrical  conductors,  then  the  current  inside  the 

x2  • 

circle  of  radius  x  is  —  i,  and  the  magnetomotive  force  which 

x2 
it  produces  is  4  TT  — 2  i.     The  magnetic  flux  per  unit  length 

"TY7  'Y* 

of  the  element  dx  is  2  if*  —  -  >  and  since  this  flux  is  associ- 

r2 

x2 
ated  with  but  —  ths  of  the  wire,  the  equivalent  elementary 

magnetic  flux  which  may  be  considered  as  linking  the  entire 
conductor  is 

-.3  J  .. 

d$2  =   2 


r 

Integrating  for  values  of  x  between  o  and  /•,  there  results 


224  TRACTION  AND  TRANSMISSION. 

Hence  the  total  magnetic  flux  linked  with  each  conductor 
of  the  two-wire  line  is 


and  therefore  the  inductance  per  centimeter  length  of  the 
straight  conductors,  being  the  flux  per  unit  current,  in  abso- 
lute units  is 

/  =  2  log€  -     -  +  -  centimeters. 
r          2 

By  reduction,  the  inductance  per  mile  for  a  single  wire 
becomes 

L  =    741  log™  -      -  +  80.5  /J  io~6  henries. 

For  copper  and  aluminum  conductors  ju  =  i. 

75.  Hyperbolic  Functions.  —  Many  numerical  calcula- 
tions in  Electrical  Engineering  are  greatly  facilitated  by 
the  use  of  hyperbolic  functions,  just  as  are  calculations  in 
mechanics  by  the  use  of  circular  functions.  The  use  of 
the  former  is  as  simple  as  that  of  the  latter  and  the  rela- 
tions which  exist  between  the  functions  of  each  type  are 
almost  identical,  the  transformation  formulae  seldom  differ- 
ing from  each  other  in  more  than  sign.  Hyperbolic  func- 
tions are  especially  useful  in  treating  the  problems  arising 
in  connection  with  transmission  lines. 

In  Fig.  96  consider  the  rectangular  hyperbola  HH  and 
the  circle  CC  concentric  with  O  as  a  center.  Since  OA 
equals  the  radius,  r,  of  the  circle,  yc/OA  is  the  circular  sine 
of  the  angle  0  by  conventional  definition.  Similarly  yh/OA 
is,  by  definition,  the  hyperbolic  sine,  or,  as  it  is  commonly 
expressed,  the  sink  of  the  corresponding  magnitude.  Al- 
though the  circular  functions  are  usually  specified  in  terms 


TRANSMISSION   LINES. 


225 


of  the  angle,  8,  included  between  the  axis  of  abscissae  and 
the  radius  vector  through  any  point,  PCJ  of  the  circle,  they 
might  equally  as  well  be  specified  by  twice  the  area  AOPC  of 
the  circular  sector  which  corresponds  with  this  angle,  if  the 


Fig.  96. 

radius  were  unity.     This  will  become  evident  if  it  be  con- 

e\ 

sidered  that  the  circular  sectorial  area  uc  =  —  Trr2,  whence 

2  7T 

d  =  -  uc;  that  is,  8  varies  directly  with  uc.     The  hyperbolic 

functions  are  not  specified  by  the  angle  8  but  by  twice  the 
hyperbolic  sectorial  area  AOPh  =  uh.  Referring  to  a  circle 
of  unit  radius,  by  definition  xc/OA  =  cos  8  =  cos  2  uc  and 
yc/xc  =  tan  2  uc;  similarly  xh/OA  =  cosh  2  uh  and  yh/xh 
=  tanh  2  u^  the  final  h  signifying  hyperbolic  functions. 
The  relations  which  exist  between  the  coordinates  of  ally 


226  TRACTION  AND   TRANSMISSION. 

point,  Ph,  on  the  hyperbola  and  the  corresponding  sectorial 

area  UH  may  be  derived  from  the  equation  of  the  equilateral 

hyperbola,  x2  —  y2  =  r2.     The  area  of  the  sector  OAPh  is 

UH  =  area  of  triangle  OQPh  —  area  of  segment  AQPh 


or 

2 

=  ^_fV*^7^ 

2           Jr 
=  -  log«  — ^- 

2  r 

Therefore  **  +  y*  =  ^  ^ 

Since  the  equation  of  the  hyperbola  may  be  written  as 

r2  =  (x  +  y)  (x  -  y), 

x  +  y         r 
whence  *•  =  —  —  > 


^  --  w 

By  adding  (i)  and  (2) 


In  general,  dropping  the  subscript  of  x,  making  the  radius 
r  =  i,  and  letting  w  =  ^^? 

^  =  i  (€«  -j_  e-«j  =  cosh  w.  (4) 

By  subtracting  (2)  from  (i)  and  expressing  in  general  form 

y  =  $(eu-t~u)  =sinhw,  (5) 

and  dividing  (5)  by  (4), 

y       sinh  u  //:\ 

^  =  -       -  =  tanh  u.  (6) 

x      cosh  u 


TRANSMISSION  LINES.  227 

The  ratio  of  the  areas,  u  =  2  uh/r*,  is  termed  the  argument, 

which  specifies  the  functions. 

For  large  values  of  u  the  second  exponential  terms  in 

equations   (4)   and   (5)  vanish  and  sinh  u  =  cosh  u  while 

tanh  u  =  i  . 

Relations  between  the  Functions.  —  The  following  useful 

formulae,  showing  some  of  the  relations  existing  between 

the  hyperbolic  functions,  may  be  derived  readily  from  the 

properties  of  .the  hyperbola  or  by  substitution  or  transfor- 

mation. 

cosh2w  —  sinh2w  =  i.  (7) 

sinh  (u  ±  v)  =  sinh  u  cosh  v  ±  cosh  u  sinh  v.  (8) 

cosh  (u  ±  v)  =  cosh  u  cosh  v  ±  sinh  u  sinh  v.  (9) 

sinh  2  u  =  2  sinh  u  cosh  u.  ,     (10) 

cosh  2  u  =  cosh2  u  +  sinh2  u.  (n) 

cosh  u  ±  sinh  u  =  e±M.  (12) 

Differential  Coefficients.  —  By  successively  differentiating 
equations  (4)  and  (5)  there  results 
dsmhu      eu  + 


.  ,  ,    >. 

=  cosh  u;  =  sinh  «,          (13) 

2 

,  \ 

=coshw.        (14) 


du  2  du2 

d  cosh  u      eu  —  e~u        .  ,  d2  cosh  u 


This  repetition  of  the  functions,  after  two  successive 
differentiations,  is  the  basis  of  their  utility  in  problems  of 
decay  or  attenuation. 

Tables.  —  An  excellent  set  of  tables  and  formulas  relating 
to  this  subject  is  published  by  the  Smithsonian  Institution 
of  Washington  in  Publication  No.  1871  bearing  the  title 
"Hyperbolic  Functions."  The  numerical  values  of  cosh 
and  sinh  for  arguments  from  o.oo  to  8.45  are  given  in  the 
following  table. 


228 


TRACTION   AND   TRANSMISSION. 


HYPERBOLIC  FUNCTIONS. 


u. 

sinh  «.  1  cosh  u. 

«. 

sinh  «. 

cosh  «. 

u. 

sinh  «. 

cosh  u. 

o.oo 

o  .  oooo 

I  .  0000 

0.50 

0.5211 

I  .1276 

1  .00 

I.I752 

I-543I 

01 

0100 

0001 

51 

5324 

1329 

05 

2539 

6038 

02 

0200 

OOO2 

52 

5438 

1383 

IO 

3356 

6685 

03 

0300 

0005 

53 

5552 

1438 

15 

4208 

7374 

04 

0400 

0008 

54 

5666 

1494 

20 

5095 

8107 

05 

0500 

0013 

55 

5782 

1551 

25 

6019 

8884 

06 

0600 

0018 

56 

5897 

1609 

30 

6984 

1.9709 

07 

0701 

0025 

57 

6014 

.1669 

35 

7991 

2-0583 

08 

0801 

0032 

58 

6131 

1730 

40 

I-9043 

1509 

09 

0901 

0041 

59 

6248 

1792 

45 

2.0143 

2488 

IO 

IOO2 

0050 

60 

6367 

1855 

50 

1293 

3524 

II 

1102 

0061 

61 

6485 

1919 

55 

2496 

4619 

12 

1203 

0072 

62 

6605 

1984 

60 

3756 

5775 

13 

1304 

0085 

63 

6725 

2051 

65 

5075 

6995 

14 

1405 

0098 

64 

6846 

2119 

70 

6456 

8283 

IS 

1506 

0113 

65 

6967 

2l88 

75 

7904 

2.9642 

16 

1607 

0128 

66 

7090 

2258 

80 

2.9422 

3-1075 

i? 

1708 

0145 

67 

7213 

2330 

85 

3-IOI3 

2585 

18 

1810 

0162 

68 

7336 

2402 

90 

2682 

4177 

19 

1911 

0181 

69 

7461 

2476 

95 

4432 

5855 

20 

2013 

O2OI 

70 

7586 

2552 

2.OO 

6269 

7622 

21 

2115 

O22I 

7i 

7712 

2628 

05 

3.8196 

3-9483 

22 

2218 

0243 

72 

7838 

2706 

10 

4.0219 

4-1443 

23 

2320 

02'66 

73 

7966 

2785 

15 

2342 

3507 

24 

2423 

0289 

74 

8094 

2865 

2O 

4571 

5679 

25 

2526 

0314 

75 

8223 

2947 

25 

6912 

4-7966 

26 

2629 

0340 

76 

8353 

3030 

3° 

4-9370 

5-0372 

2? 

2733 

0367 

77 

8484 

3U4 

35 

5-I95I 

2905 

28 

2837 

0395 

78 

86l5 

3199 

40 

4662 

5569 

2Q 

2941 

0423 

79 

8748 

3286 

45 

5-7510 

5-8373 

30 

3045 

0453 

80 

888l 

3374 

50 

6.0502 

6.1323 

31 

3150 

0484 

81 

9OI5 

3464 

55 

3645 

4426 

32 

3255 

0516 

82 

9150 

3555 

60 

6.6947 

6  .  7690 

33 

336o 

0549 

83 

9286 

3647 

65 

7.0417 

7.1123 

34 

3466 

0584 

84 

9423 

3740 

70 

4063 

4735 

35 

3572 

0619 

85 

956i 

3835 

75 

7  •  7894 

7.8533 

36 

3678 

0655 

86 

9700 

3932 

80 

8.1919 

8-2527 

37 

3785 

0692 

87 

9840 

4029 

85 

8.6150 

8.6728 

38 

3892 

0731 

88 

0.9981 

4128 

90 

9.0596 

9.1146 

39 

4000 

0770 

89 

i  .0122 

4229 

95 

9.5268 

9-5791 

40 

4108 

0811 

90 

0265 

433i 

3.00 

10.0179 

10.0677 

4i 

4216 

0852 

9i 

0409 

4434 

05 

10.5340 

10.5814 

42 

4325 

0895 

92 

0554 

4539 

IO 

11.0765 

11.1215 

43 

4434 

0939 

93 

0700 

4645 

15 

11.6466 

11.6895 

44 

4543 

0984 

94 

0847 

4753 

20 

12.2459 

12.2866 

45 

4653 

1030 

95 

0995 

4862 

25 

12.8758 

12.9146 

46 

4764 

1077 

96 

1144 

4973 

30 

13-5379 

I3.5748 

47 

4875 

1125 

97 

1294 

5085 

35 

14-2338 

14.2689 

48 

4986 

1174 

98 

1446 

5199 

40 

14.9654 

14-9987 

49 

5098 

1225 

99 

1598 

53U 

45 

iS-7343 

15.  7661 

TRANSMISSION   LINES. 


229 


HYPERBOLIC  FUNCTIONS. 


u. 

sinh  u. 

cosh  u. 

u. 

sinh  ».    |    cosh  u. 

3.50 

16.5426 

16.5728 

6.00 

201.7132 

201.7156 

55 

17.3923 

17.4210 

05 

212.0553 

212.0577 

60 

18.2855 

18.3128 

IO 

222.9278 

222.9300 

65 

19.2243 

19  .  2503 

15 

234.3576 

234.3598 

70 

20.2113 

2O.  2360 

20 

246.3735 

246.3755 

75 

21.2488 

21.2723 

25 

259.0054 

259.0074 

80 

22.3394 

22.3618 

30 

272.  2850 

272.2869 

85 

23.4859 

23.5072 

35 

286.2455 

286.2472 

90 

24.6911 

24.7113  - 

40 

300.9217 

300.9233 

3-95 

25.958I 

25-9773 

45 

316.3504 

316.3520 

4.00 

27.2899 

27.3082 

So 

332.5700 

332.5716 

05 

28.6900 

28.7074 

55 

349.6213 

349.6228 

10 

30.1619 

30.1784 

60 

367.5469 

367.5483 

15 

31.7091 

31.7249 

65 

386.3915 

386.3928 

20 

33-3357 

33.3507 

7o 

406  .  2023 

406.2035 

25 

35-0456 

35.0598 

75 

427.0287 

427.0300 

30 

36-843  i 

36-8567 

80 

448.9231 

448.9242 

35 

38.7328 

38.7457 

85 

471-9399 

47L94IO 

40 

40.7193 

40.7316 

90 

496.1369 

496.1379 

45 

42.8076 

42.8193 

6-95 

521.5744 

521.5754 

50 

45  •  °°30 

45.0141 

7.00 

548.3161 

548.3170 

55 

47.3109 

47.32I5 

05 

576.4289 

576.4298 

60 

49-7371 

49-7472 

10 

605.9831 

605.9839 

65 

52-2877 

52.2973 

15 

637.0526 

637.0534 

70 

54.9690 

54.9781 

20 

669.7150 

669.7157 

75 

57.7878 

57^965 

25 

704.0521 

704.0528 

80 

60.7511 

60.7593 

30 

740.1497 

740.1504 

85 

63.8663 

63.8741 

35 

778.0980 

778.0986 

90 

67.  1412 

67.1486 

40 

817.9919 

817.9925 

4-95 

70.5839 

70.5910 

45 

859.93I3 

859.9318 

5.00 

74.2032 

74  •  2099 

50 

904.0210 

904.0215 

05 

78.0080 

78.0144 

55 

950.37H 

950.3716 

10 

82.0079 

82.0140 

60 

999.0976 

999.0981 

15 

86.2128 

86.2186 

65 

1050.323 

20 

90.6334 

90.6389 

70 

1104.174 

25 

95-2805 

95.2858 

75 

1160.780 

30 

100.1659 

100.  1709 

80 

1220.301 

35 

105.3018 

105-3065 

85 

1282.867 

40 

110.7009 

110.7055 

90 

1348.641 

45 

116.3769 

116.3812 

7-95 

1417.787 

5° 

122.3439 

122.3480 

8.00 

1490.479 

55 

128.6168 

128.6207 

05 

1566.698 

60 

135-2114 

135-2150 

IO 

1647  .  234 

65 

142.1440 

142.1475 

15 

1731.690 

70 

149.4320 

149.4354 

20 

1820.475 

75 

157-0938 

157.0969 

25 

1913.813 

80 

165.  1482 

165.1513 

30 

2OII  .936 

85 

173.6158 

173.6186 

35 

2115.090 

90 

182.5173 

182.5201 

40 

2223.533 

95 

191.8754 

191.8780 

45 

2337-537 

230 


TRACTION   AND  TRANSMISSION. 


76.  Line  Capacity.  —  To  determine  the  capacity  of  a 
transmission  line,  consider  two  wires  of  indefinitely  small 
diameters  placed  df  centimeters  apart  and  having  respec- 
tively charges  of  +  q  and  —  q 
units  per  centimeter  length  of 
conductor.  The  intensity  of 
-  the  electric  field  at  a  point  P, 
Fig.  97,  distant  r\  cm.  from  one 
wire  and  r^  cm.  from  the  other, 
that  is,  the  electrostatic  flux  per  unit  area  of  equipo- 
tential  surface  or  force  exerted  upon  a  unit  positive  charge 
at  this  point  due  to  the  charge  on  wire  A  alone,  is 

and  that  due  to  the  charge  on  wire  B  alone  is 


Representing   the  potential  at   the  point   P  due   to   the 
charge  on  A  by  V &,  and  that  due  to  the  charge  on  B  by  VB, 
it  follows  from  the  definition  of  potential  that 
dVA      2  q 


and 


dVB  _  _2_2 


where  k  is  the  permittivity  or  specific  inductive  capacity 
of  the  dielectric.  If  the  potentials  at  the  point  0  midway 
between  the  two  very  small  wires  due  to  their  charges  be 
respectively  V  A  and  VB ',  then  the  potential  difference 
between  P  and  0  is  the  sum  of 


TRANSMISSION  LINES.  231 


and 


-  VB'  =  P  - 

J 


Or,  since  for  the  point  O,  VA'  +  VB   =  o,  the  potential  at 
P  due  to  the  charges  on  both  wires  is 

VA+VB  =  V=2-f\o^-  (i) 

For  any  point  to  be  on  the  equipotential  surface  which 
passes  through  the  point  P,  the  ratio  of  its  distances  from 
B  and  A  respectively  must  be  constant.  The  locus  of  a 

point  P  which  moves  so  that  —  is  constant  is  a  circle,  and 

r\ 

if  C  be  its  center  and  r  its  radius,  then 

CA  X  CB  =  r\  (2) 


Fig.  98. 

From  Fig.  98,  which  is  drawn  in  accordance  with  equa- 
tion (2),  it  appears  that  triangles  ACP  and  BCP  with  the 

CA        r 

common  angle  at  C  are  similar,  since  from  (2)  —  =  —  —  • 

Y        Ox? 

Therefore 

AP      BP  r 


and 

r 


CA      CP  CA 

CA      ri 


232 


TRACTION  AND   TRANSMISSION. 


which  shows  that  —  is  constant  whatever  the  position  of  P 
r% 

on  the  circle.  Consequently  the  equipotential  surfaces  re- 
sulting from  the  charges  on  the  two  wires  A  and  B  are 
cylindrical  in  shape  and  are  not  coaxial  with  those  wires; 
furthermore,  the  axes  of  such  cylinders  of  different  radii  are 
not  coincident.  The  radius  of  the  zero  potential  surface 
which  passes  through  the  mid-point  0  must  be  infinitely 

large  (for  —  =  i ),  and  therefore  this  surface  is  a  neutral 
\       r2        / 

plane  which  bisects  the  line  AB  at  right  angles.  All  the 
equipotential  surfaces  to  the  left  of  this  plane  surround  A 
and  those  to  the  right  surround  B. 

Consider    two    equipotential    surfaces    surrounding    the 
wires  A  and  B  to  be  replaced  by  solid  cylindrical  conductors 


Fig.  99- 

of  radii  ai  and  a2  respectively,  Fig.  99,  and  carrying  charges 
respectively  of  +  q  and  —  q  units  per  centimeter  length  of 
conductor.  Such  substitution  does  not  alter  the  potential 
or  electric  flux  distribution  beyond  these  surfaces.  The 
potentials  of  the  wires  are  respectively 

2_q         EM 

k        'AM 


V1 


TRANSMISSION  LINES.  233 

AN 


and 


Therefore  their  potential  difference  is 


But  from  the  figure 

BM  =  BM'  =  BCi 
AM  ~  AM'  ~    ai 

AN     AN'      AC2 


also  AC2  X  BC2  = 

consequently 


Furthermore, 

BCi  (Bd  -  d'}  =  a? 
and  BC2  (BC2 

whence 
and 

Therefore  the  capacity  per  centimeter  length  of  line  having 
two  cylinders  of  radii  #1  and  #2  as  conductors  is,  from  (3), 

k 


234 


TRACTION  AND  TRANSMISSION. 


If  both  wires  have  the  same  diameter,  r  =  a\  =  #2,  and 
the  capacity  is 

C  =  -  *  (4) 


2loge 


Representing  the  distance  between  conductor  axes  by  d,  it 
is  seen  that 


v/ 

\ 


whence  df  =  Vd2  —  4  r2. 

Therefore  the  capacity  of  a  transmission  line  having  con- 
ductors of  r  centimeters  radius  is 

k 


d 


C  = 


or,  letting  --  =  m,  this  becomes 
2  r 


C  = 


-  4 


2  log. 

M-V/'-i 

2  loge 

"(x+v/'-s)' 

m2 

i  -  \A  -  £ 

TRANSMISSION  LINES.  235 

This  may  also  be  expressed  as 

k 

C  =  -  —    electrostatic  units. 

4  cosh  l  m 

Reducing  to  microfarads  per  mile,  the  capacity  of  either 
wire  with  respect  to  the  neutral  plane  is 

c  =  0.0388  k  ^ 

Iogi0(w  +  Vm2  —  i) 


^  O.OoO^  "  t/-\ 

or  C  =  -    -^—-  -  (6) 


77.   Equations  of  Wave  Propagation  along  Wires.  —  Any 

polyphase  transmission  line  can  be  resolved  into  separate 
single-phase  single-wire  circuits  with  imaginary  perfectly 
conducting  ground  return  paths.  Thus,  the  voltage  on  a 

representative  single-wire  circuit  of  a  three-phase  trans- 

-p 
mission  line  with  E  volts  between  wires  is  — - ,  which  is  the 

^3 

voltage  from  one  conductor  to  neutral.  Such  a  line  trans- 
mits one-third  of  the  total  power.  It  is  therefore  only 
necessary  to  consider  the  current  and  voltage  distribution 
on  a  single-wire  circuit. 

Consider  the  element  ds  of  a  uniform  line  with  a  per- 
fectly conducting  ground  return  circuit,  at  a  distance  s  from 
the  end  upon  which  an  alternating  electromotive  force  is 
impressed,  as  shown  in  Fig.  100.  A  current  will  flow 
through  the  conductor,  which  at  a  given  instant  /  at  the 
element  ds  may  be  represented  by  /',  and  that  in  the  ad- 
jacent elements  by  I'  +  dlf  and  /'  —  dl',  the  latter  refer- 
ring to  the  next  adjacent  element  more  remote  from  the 
generator.  Let  E'  be  the  potential  at  this  instant  of  the 


236  TRACTION  AND  TRANSMISSION. 

line  with  respect  to  the  earth  at  the  element  ds,  and  let 
the  potentials  of  the  adjoining  elements  be  Ef  +  dE'  and 
Ef  —  dE'  respectively.  Let  R,  L,  and  C  in  homologous 

i  I'  il-dl' 


Fig.  100. 

units  represent  respectively  the  uniformly  distributed  re- 
sistance, inductance,  and  capacity  per  unit  length  of  the 
line. 

The  difference  of  potential  between  the  two  ends  of  the 
element  ds  is  dE'  ',  and  this  must  be  equal  to  the  sum  of  the 
resistance  and  inductance  reactions  of  the  elementary  line 
section  occasioned  by  the  current  /'  ';  consequently  for  this 
element 


Since  the  line  has  capacity  with  respect  to  the  earth,  it 
takes  a  charging  current;  and  in  addition  a  slight  leakage 
current  may  flow.  Therefore  the  current  which  does  not 
continue  beyond  the  element  ds,  but  which  flows  from  the 
line  to  ground  under  the  voltage  £',  is 


-dE' 
at 


TRANSMISSION  LINES.  237 

where  g  is  the  leakance  or  the  reciprocal  of  the  insulation 
resistance  per  unit  length  of  line.     Then 

dlf         dE' 


Differentiating  (i)  with  respect  to  time  and  (2)  with 
respect  to  distance,  there  result  respectively 


d2!'       Rdl^  =       A(d&\  =        < 
"  dt?  dt  ''        dt(ds)          ds\dt 

d2!'      n  d  (dE'\  .      dE' 

and      --TT  *=  CT  \~^7  )  +  £  ~7~  * 
ds2          ds\  dt  /          ds 

Substitution  of  the  former  in  the  latter  equation  gives 
d2!'  d*I'  dl'         dE' 


ds2  dt2  dt  ds 

and  replacing  the  last  term  by  its  equivalent  from  (i) 
there  is  obtained  the  differential  equation  of  current  propa- 
gation along  a  line  as 

(3) 


Similarly,  by  differentiating  (i)  with  respect  to  distance 
and  (2)  with  respect  to  time,  and  combining  the  resulting 
expressions,  there  results  the  differential  equation  of  volt- 
age propagation  as 


Equations  (3)  and  (4)  are  identical  as  to  /'  and  £',  and 
their  solution  indicates  the  current  and  voltage  values  at 
the  point  distant  s  from  the  generator  at  the  time  t  in 
terms  of  the  line  constants.  This  general  equation  refers 
to  any  circuit  with  distributed  capacity  and  inductance, 


238  TRACTION  AND  TRANSMISSION. 

and  its  solution  is  of  importance  in  telephonic  and  power 
transmission  problems. 

78.  Attenuation  and  Wave-Length  Coefficients.  —  The 
solution  of  the  equation  of  wave  propagation  may  readily 
be  effected  by  not  considering  the  short  unsteady  period 
immediately  following  the  application  of  voltage  to  the  line, 
for  then  the  solution  may  be  simplified  by  the  introduction 
of  the  complex  quantity  which  results  in  the  elimination  of 
the  time  variable.  The  resulting  expressions  are  complex 
quantities  and  their  interpretation  must  be  made  accord- 
ingly. 

Introducing  the  quadrantal  operator,  j  =  V—  i,  and 
counting  the  distance  5  positive  from  the  receiving  end  of 
the  line,  equations  (i)  and  (2)  of  §  76  for  the  steady  state 
may  be  written* 

)!,,  (i) 


and  =(g+/«O3.,  (2) 

where  Em  and  Im  represent  the  maximum  (or  effective) 
values  of  electromotive  force  and  current  at  any  point  on 
the  circuit,  (R  +  juL)  is  the  conductor  impedance,  and 
(g  -f-  7'coC)  is  the  dielectric  admittance.  Differentiating 
either  of  these  expressions  and  substituting  the  other  in  the 
result  yields  respectively 


=  (R+  juL)  (g  +  juty  Em  =  y2Em  (3) 

as* 

JIT 
and 


*  See  p.  74,  Alternating  Current  Machines  (1908)  by  Sheldon,  Mason, 
and  Hausmann. 


TRANSMISSION  LINES.  239 

where  y2  =  (R  +  juL)  (g  +  jwC)  for  convenience.  Equa- 
tions (3)  and  (4)  are  identical  equations  as  to  Em  and  Im 
and  differ  only  in  the  terminal  conditions,  consequently  the 
solution  of  one  will  suffice. 

Considering  equation   (4)   and  multiplying  through  by 

2  —  -  3  there  results 


_    „ 

ds     df  '      7    m  ds 

which  when  integrated  becomes 


d  s 

Replacing  the  constant  of  integration  c\  by  T2^2,  where  c2 
is  also  a  constant,  and  separating  the  variables,  there  results 


Integration  yields 

loge  [c,  (/_  +  VV  +  rf)]-  75, 

where  c3  is  another  constant  of  integration.     Writing  in 
exponential  form,  this  equation  becomes 

+  C22)  c3. 


Squaring,        /.*  +  ft'  -        +  /J  -  2  / 

^3 

£27S  €T* 

or  —  -  c22  =  2/m—  ; 

Cs  c3 

whence 


o 

where  the  two  constants  are  A  =  -  and  B  =  —  -  • 

2C3  2 

Since  the  exponential  coefficient  7  is  the  square  root  of 


240  TRACTION  AND  TRANSMISSION. 

the  product  of  two  complex  numbers,  it  also  is  a  complex 
quantity,  and  may  be  written 

y  =  (3+ja,  (6) 

where  0  and  a  are  its  two  rectangular  components.     Then 

/s2  +  2jap  +jw  =  (R  +j<*L)  (g  +y«o, 

or       (/32  -  a2)  +  2  j<tf  =  (Rg  -  a,2CL)  +y  (guL  +uRC). 
This  equation  can  be  true  only  if 


and  if  2a/3  = 

These  are  simultaneous  equations  which  can  be  solved  for 
a  and  /3.  Thus,  substituting  the  value  of  a  from  the  latter 
in  the  former  gives  the  biquadratic 


whence 


=  o; 
4 


and  _  _ 

p  =  v'i  [  V(<W  +  g2)  (*2  +  o,2L2)  -  ofLC  +  Rg]  ;    (7) 
similarly 


«  =  \/i  [V(co2C2  +  g2)  (#2  +  W2L2)  +  co2LC  -  12g].  (8) 

The  constant  /3  is  called  the  attenuation  coefficient,  and  a  is 
called  the  wave-length  constant.  These  constants  give  the 
value  of  7  in  equation  (5)  for  the  current  at  any  point  of 
the  line. 

79.  Current  and  Voltage  Distribution  on  Lines.  —  Ap- 
plying hyperbolic  functions  to  equation  (5)  of  the  fore- 
going paragraph  for  the  current  on  a  line  at  a  point  distant 
s  from  the  receiving  end,  there  results 

Im  =  A  (cosh  js  +  sinh  ys)  —  B  (cosh  ys  —  sinh  ys). 
=  (A  -  B]  cosh  ys  +  (A  +  B)  sinh  ys.  (i) 


TRANSMISSION   LINES.  241 

The  voltage  at  the  same  point  is  found  by  differentiating 

(i)  with  respect  to  distance  and  substituting  —7^  in  equa- 

ds 

tion  (2)  of  §  78.     Since 

—  cosh  ys  =  7  sinh  ys 
ds 

—  sinh  ys  =  7  cosh  7$, 
ds 


[(A  -  B)  sinh  7*  +  (A  +  B)  cosh  ys].    (2) 

The  constants  A  and  .#  of  equations  (i)  and  (2)  may  be 
determined  from  the  conditions  at  the  receiving  end  of  the 
line.  Let  Er  and  Ir  be  the  maximum  (or  effective)  values 
of  the  voltage  and  current  at  this  terminal.  Then  for 
s  =  o,  since  cosh  (o)  =  i,  and  sinh  (o)  =  o, 

Ir   =   A    ~  B 

and  Er 

Substituting  these  values  in  (i)  and  (2)  yields 

/„  =  Ir  cosh  75  +  Er  p,   •?"   sinh  ys  (3) 

K  +jaL 

and  Em  =  Er  cosh  ys  +  Ir      ,    ?"  sinh  7^.  (4) 


When  s  is  reckoned  from  the  generator  toward  the  re- 
ceiving end  of  the  line,  these  equations  become 

Im  =  Ia  cosh  75  -  E0       .J.      sinh  7*  (5) 


242  TRACTION   AND  TRANSMISSION. 

and  Em  =  Eg  cosh  7*  -  Ig      ,    /"  sinh  75.  (6) 

g  +juC 

The  hyperbolic  functions  of  the  complex  quantity  7  may 
be  written 

cosh  75  =  cosh  (ps  +jas)  =  cosh  (3s  •  cos  as  +j  sinh  PS  •  sin  as 
and 

sinh  js  =  sinh  (3s  •  cos  as  -\-j  cosh  /fo  •  sin  as. 

The  terminal  conditions  in  any  special  problem  are  usu- 
ally specified,  the  voltage  being  considered  the  reference 
phase.  In  the  present  notation  for  vector  rotation  a  cur- 
rent leading  the  voltage  is  written  ii  +  jiz  and  a  lagging 
current  is  represented  by  ii  —  ji%. 

From  equation  (5)  it  is  seen  that  for  an  infinitely  long 
line,  on  which  the  current  at  the  inaccessible  end  is  zero, 

p+ja 


which,  when  substituted  in  the  same  equation,  gives  the 
current,  at  a  point  distant  s  from  the  generator  end  of 
such  a  line,  as 

Im  =  Ia  (cosh  ys  —  sinh  75)  =  Ige~y8. 
Similarly    En  =  Ett  <•-*•  =  E^T*". 

The  exponential  function  with  the  imaginary  exponent 
may  be  written  in  the  trigonometric  form  by  means  of  the 
expression 

e±y««  =  cos  as  ±j  sin  aSt 

If  a  point  r  be  chosen  on  this  long  line  so  that  the  distance 
between  it  and  the  point  s  will  be  an  integral  number  of 
wave  lengths,  n,  then 

cos  as  —  j  sin  as  =  cos  ar  —  j  sin  ar\ 


TRANSMISSION  LINES.  243 

consequently  as  +  2  irn  =  ar. 

Then  the  wave  length  herefrom  is 

_  r  ~  s  —  2  v 

A  —  "~       ~  —          • 

n  a 

As  the  frequency  of  the  impressed  electromotive  force  is 
-  cycles  per  second,  the  velocity  of  wave  propagation 

2  7T 

will  be  co  _       co 

v  =  — X  =  -• 

2  7T  a 

The  expression  for  a  in  terms  of  the  line  constants  is  given 
in  §  78.  For  a  perfectly  insulated  resistanceless  line 
a  =  w  VLC,  and  the  velocity  of  wave  propagation  is  that 
of  light,  namely  3  X  io10  centimeters  per  second,  or  186,000 
miles  per  second. 

80.  Regulation.  —  The  voltage  regulation  of  a  trans- 
mission line  is  the  ratio  of  the  voltage  variation  at  the 
receiving  end  between  no  load  and  full  non-inductive  load 
to  the  full-load  voltage  at  the  same  end  of  the  line  for 
constant  impressed  voltage  at  the  other  end. 

When  the  transmission  line  is  open-circuited  at  the  re- 
ceiving end,  the  current,  Igo,  entering  it  at  the  generator, 
called  the  charging  current,  is  obtained  from  equation  (5) 
of  the  preceding  article  ior  s  =  S  =  total  length  of  the 
line,  by  placing  Im  =  o. 

0+ja       sinh  yS 

Inen  lgo  =  h,g—— — — :  •  — r — -• 

R  +jwL    cosh  75 

0.  sinh  y5  ,      0 

Since  — r-—  =  tanh  yS, 

cosh  7-S 

this  becomes        I0o  =  Eg  £  "l"-?a_  tanh  yS.  (i) 

K 


244  TRACTION  AND  TRANSMISSION. 

Substituting  this  value  for  Ig  in  equation  (6)  of  §  79,  there 
results  the  voltage  at  any  point  distant  s  from  the  gen- 
erating end  of  the  line  as 

E0  =  Eg  (cosh  ys  —  sinh  ys  •  tanh  yS),  (2) 

and  the  voltage  at  the  receiving  end  for  5  =  S  as 

Ero  =  Eg  (cosh  75  —  sinh  yS  •  tanh  7,5), 
or,  since  cosh2  yS  —  sinh2  yS  =  i, 


as 


The  regulation  of  the  transmission  line  is  then  expressed 

_       ,   ..          Ern  -  Er      Eg  sech  yS  -  Er  ,  . 

Regulation  =     r°        -  =  -«  --  ^  -  r-          (4) 


81.  Numerical  Illustration.  —  Let  it  be  required  to  trans- 
mit 10,000  kilowatts  at  60  cycles  over  a  three-phase  aerial 
transmission  line  300  miles  long,  employing  stranded  alu- 
minum conductors  0.63  inch  in  diameter  of  area  0.236 
square  inch,  triangularly  spaced  with  9  feet  interaxial  dis- 
tance. The  voltage  at  the  receiving  end  of  the  line  is  to 
be  100,000  volts  between  conductors,  and  the  power  factor 
of  the  load  is  85  per  cent  lagging.  Determine  the  voltage 
to  be  impressed  on  the  line,  the  entering  current,  the  effi- 
ciency of  transmission,  the  voltage  regulation  of  the  line, 
and  the  charging  current. 

The  constants  per  mile  of  a  representative  single  circuit 
with  a  perfectly  conducting  ground  return  path  and  carry- 
ing one-  third  of  the  total  energy,  are 

R  =  0.30  ohm, 

L  =  0.00196  henry, 

C  =  0.0153  X  io~6  farad, 

g  =  practically  zero. 


TRANSMISSION  LINES.  245 

The  current  per  single  circuit  (or  per  wire)  at  the  load 
end  is 

10,000,000 
Ir  =  -  •  -  •  -  —  =  68.  o  amperes. 

3XX0.85 


or     Ir  =  68.0  [0.85  -7  sin  (cos"1  0.85)]  =  57.8  -  35.87; 

IOO  OOO 

the  voltage  at  the  receiving  end,  namely  -         -  or  57,700 

^3 
volts  per  phase,  being  considered  the  datum  phase. 

The  attenuation  and  wave-length  constants  per  mile  for 
a  frequency  of  60  cycles  (whence  co  =  377)  are  respectively 

|8  =  V  2.88(^0.090  +  0.5476  —  0.74)  X  io~3  =0.000412 
and  a  =  A/2.  88  (0.799  +  o.74o)X  io~3  =  0.00210. 

The  hyperbolic  and  circular  functions  respectively  of  'f$s 
and  as  for  the  total  length  of  the  transmission  line  are 

cosh  (0.1236)  =  1.00765     cos  (0.630)  =  cos  36°  6'=  0.8080 
sinh  (0.1236)  =  0.1239       sm  (0-630)  =  0.5892. 

The  current  at  the  generator  end  of  the  line  may  then  be 
obtained  from  equation  (3)  of  §  79  as 

I0  =  (57-8  -  35.87X1.00765  X  0.8080  +  0.1239X0.5892;) 


or 

itt  =(57-8  -  35-8.7)  (0.8142  +  0.06057) 

-f  90.5  (1.678  -h  0.3257)  (o.iooi  +  0.59377') 
=  49.2  -  25.657  +  90.5  (-  0.0249  +  1.0277) 
=  46.95  +  67.257  amperes, 

and  the  current  from  the  generator  per  wire  is  82.0  amperes. 


246 


TRACTION  AND  TRANSMISSION. 


Similarly  the  voltage  at  the  generator  end  of  the  trans- 
mission line  is 

S  (o-iooi  +  0.59377) 


^  =  (57-8  -  35.87) 

+  57,700  (0.8142  +  0.06057) 
=  (57-8  -  35-87)  (0.364  ~  0.071  57)  (o.iooi  +0.59377)  io3 

+  (46.95  +  349  jO  !03 
=  (12.04  +  9-237  +  46.95  +  3-49.7)  Io3 
=  58,990  +  12,7207", 

and  the  voltage  per  single  circuit  to  be  impressed  on  the 
line  in  order  to  have  57,700  volts  per  phase  at  the  receiving 
end  is  60,400  volts. 


Fig.  iox. 


The  vector  diagram,  Fig.  101,  exhibits  the  phase  rela- 
tions of  the  voltages  and  currents  at  the  ends  of  the  line. 
It  is  seen  herefrom  that  the  current  at  the  generator  end 
leads  the  voltage  at  the  same  place  by  the  angle  (55°  4'  — 
12°  250,  or  42°  39'. 

The  efficiency  of  transmission  at  full  load  is 

57,700  X  57.8 
-  -  '  '        —     —  — 


f    o     A 
60,400  X  82.0  cos  (42°  39') 


j  or  9I-5  Per  cent- 


TRANSMISSION  LINES.  247 

Since  cosh  yS  =  0.8142  +  0.06057,  tne  voltage  at  the 
receiving  end  on  open  circuit  for  the  same  impressed  E.M.F. 
at  the  generator  end  is 

+  12,7207* 

+  o.o6o5y  =  74'100  +  I0'3°°>' 

and  the  absolute  value  is  74,900  volts.  Consequently  the 
voltage  regulation  of  the  transmission  line  for  85  per  cent 
power  factor  is 

74,900  -  57,700  =  or 


The  charging  current  per  single  circuit  or  per  wire  is 
obtained  from  equation  (i)  of  §  80  as 

T        (  o  .x/o.412  +  2.1  A/O.IOOI  +  0.15037  A 

/„„  =  (58.990+  12.7207)   -  .)(.-  ~7^ 

\o.30  +  0.7477X0.8142  +  0.060577 

=  (140.2  +  30.37)  (1.678  +  0.3257)  (0.1174  +  0.4777) 

=  -19.5  +  119.57, 

and  the  absolute  value  is  1  2  1  amperes,  and  leads  the  voltage 
Er  by  99°  1  6'.  Therefore  the  charging  current  at  the  gen- 
erating end  of  the  line  leads  the  voltage  at  the  same  place 
by  the  angle  99°  16'  -  12°  25',  or  by  86°  51'. 

82.  Corona  Loss.  —  It  is  found  by  experiment  that  the 
corona  loss  on  a  transmission  line  is  proportional  to  the 
square  of  the  excess  voltage  over  the  critical  value  at 
which  corona  is  initiated  and  also  to  the  frequency;  thus 
the  loss  per  mile  in  watts  on  a  single-wire  ground-return 
circuit  is  quite  closely 

P  =  0.024  }(Em-Ecr)\  (i) 

where  Em  is  the  voltage  (effective  value  in  kilovolts)  from 
conductor  to  neutral  at  any  point  on  the  line  distant  s 
miles  from  its  generator  end,  and  Ecr  is  the  effective  value 
of  the  voltage  at  which  corona  appears.  This  equation  is 


248  TRACTION  AND  TRANSMISSION. 

similar  to  that  formulated  by  Dr.  Steinmetz.  On  a  single- 
phase  line  and  on  a  three-phase  line  (for  corona  loss  per 
phase)  the  factor  (Em  —  Ecr)2  is  respectively  four  and  three 
times  as  large  as  for  a  single- wire  circuit. 

Frequently  portions  of  transmission  lines  are  located  in 
high  altitudes,  where  the  critical  voltage  is  lower  than 
normal,  and  corona  loss  ensues,  which  can  be  calcu- 
lated from  the  foregoing  expression.  The  factor  0.024  is 
fairly  constant;  it  does  not  depend  on  atmospheric  pres- 
sure, size  of  wire,  or  conductor  spacing,  but  it  does  seem 
to  be  influenced  by  the  presence  of  smoke,  dust,  and  snow 
in  the  air.  Additional  experimental  verification  of  this  nu- 
merical constant  is  very  desirable.  The  method  of  measur- 
ing corona  loss  is  by  means  of  a  wattmeter,  the  current 
coil  of  which  is  connected  directly  in  the  transmission 
line  at  the  neutral,  which  is  grounded,  and  the  potential 
coil  of  the  wattmeter  is  connected  to  the  high-potential 
transformer  coil. 

An  important  consideration  arises  when  the  distant  end 
of  a  transmission  line  is  open-circuited,  for  then  the  voltage 
at  every  point  on  the  line  increases,  and  the  potential  over 
a  considerable  portion  of  the  circuit  exceeds  the  critical 
voltage,  and  consequently  a  loss  of  energy  ensues.  This 
loss  begins  at  that  point  where  the  voltage  E0  is  just  equal 
to  the  critical  value  Ecr,  and  becomes  greater  and  greater 
as  the  far  end  is  approached.  The  voltage  at  any  point  on 
an  open-circuited  line  is  given  by  equation  (2)  of  §  80. 
By  substituting  various  values  of  s  therein,  and  plotting 
the  corresponding  values  of  E0  in  terms  of  distance,  a 
voltage-distribution  curve  for  the  particular  line  will  result. 
From  this  voltage-distance  curve  can  be  seen  the  distance, 
$o,  from  the  generator  end  of  the  transmission  line  at 


TRANSMISSION  LINES. 


249 


which  corona  begins.  Of  course,  this  equation  might  be 
solved  for  $0,  but  not  knowing  the  phase  of  voltage  E0  at 
the  end  of  this  part  of  the  circuit,  this  plan  leads  to  diffi- 
culty when  applying  the  resulting  expression  to  the  solu- 
tion of  actual  problems. 

In  order  to  determine  the  total  corona  loss  on  a  repre- 
sentative single-wire  open- 
circuited  line,  consider  an 
element  ds  of  the  circuit, 
distant  s  miles  from  the 
point  SQ  where  corona  be- 
gins, for  which  the  excess 
voltage  is  Em  —  Ecr  kilo- 
volts;  Fig.  102.  The 
power  loss  over  this  elementary  line  section  in  watts  is 

dP  =  0.024  f(Em-  Ecr)*ds, 
and  over  the  entire  distance  I  =  S  —  s0  the  loss  is 


P  =  0.024  /       (Em-  Ecryds. 
J  o 

But  from  the  equation  referred  to, 

Em  =  Ecr  (cosh  ys  —  sinh  75  tanh  yl)  ; 
therefore 

P  =  0.024  fEcr2  I    (cosh  ys  —  sinh  ys  tanh  yl  —  i)2ds, 

JQ 

or 

P  =  0.024  JECA    I    cosh2  ys  ds  —  2  tanh  yl  I    sinh  75  cosh  ys  ds 
LVo  JQ 

—  21    cosh  ys  ds  +  tanh2  yl  I    sinh2  ys  ds 
JQ  JQ 

+  2  tanh  yl  I    sinh  75  ds-{-   I    ds  . 
Jo  JQ 


250  TRACTION  AND  TRANSMISSION. 

Upon  integration  this  equation  becomes 

P*=o.oi2 - Ecr2  [sinh  yl  cosh  yl  -\-  yl  —  tanh  yl  (cosh  2  yl  —  i) 

—  4  sinh  yl  +  tanh2  yl  (sinh  7/  cosh  yl  —  yl) 
+  4  tanh  7^  (cosh  ?/  —  i)  +  2  yl], 

and  when  simplified  reduces  to 


Ps  T~*  91 1         ^  tann  7'  197!         /  \ 

=  o.oi2jEc/l\  3  —  - — —  —  tanh27/  (2) 

yl 

as  the  expression  for  the  total  corona  loss  in  watts  on  an 
open-circuited  single-wire  earth-return  circuit. 

Thus  for  the  140,000- volt,  io,ooo-K.W.,  5oo-mile,  6o-cycle, 
three-phase  transmission  line  of  §  72,  with  No.  oooo  stranded 
aluminum  conductors  placed  15  feet  apart,  the  line  con- 
stants per  mile  on  a  representative  single-wire  circuit  which 
transmits  one-third  of  the  total  energy,  are 

R  =  0.463  ohm  (includes  resistance  increase  due  to  skin 

effect  and  stranding), 
L  =  0.00218  henry, 
C  =  0.0137  microfarad. 
g  is  negligibly  small  =  o. 

The  attenuation  and  wave-lengths  constants  are  respectively 

/3  =  0.000563 
and 

a  =  0.00214; 
whence 

7  =  0.000563  +  0.002147. 

It  will  be  observed  that  severe  conditions  are  assumed  in 
order  to  bring  out  the  results  more  forcibly. 

When  the  line  is  open-circuited  at  the  receiving  end,  the 
voltages  in  terms  of  the  impressed  voltage  Ea  at  several 


TRANSMISSION  LINES. 


251 


points  on  the  line,  as  determined  from  equation  (2)  of  §  80, 
are  given  in  the  following  table: 


Distance  from  gener- 
ator (miles). 

Eo 
Eg 

Eo 
Eg 

40 

.092—O.II2y 

.10 

IOO 

.2I2—O.  265.7 

.24 

200 

.382-0.487; 

.46 

300 

.503-0.  658  j 

.64 

400 

•  575-0-  764  j 

•75 

-500 

.600-0.  799  j 

•79 

Thus,  for  a  factor  of  safety  of  i.i,  the  length  of  line  over 
which  corona  appears  is  460  miles.  The  total  power  loss  in 
watts  per  phase  into  the  air  is  therefore,  from  equation  (2), 


p=  0.012  x  60 
-  (-0.990 


460  x  [3  -(4.050  -  i.i4y) 


or 


P=  0.72  X  ^^  X  460  X  0.65  =  1700  k.w., 

IOOO 


which  is  equivalent  to  a  current  of 


1700 


140 


-^  ,  or  2 1  amperes 


per  phase.     This  current  value  almost  equals  the  full-load 

current  of  -  ,  or  23.8  amperes,  which  would  enter 

140X3 

this  unusually  long  transmission  line.  To  this  must  be 
added  at  right  angles  the  charging  current  due  to  the 
capacity  of  the  line.  Thus,  an  ammeter  at  the  power 
house  which  supplies  energy  to  this  circuit  would  indicate 
approximately  the  same  current  when  the  far  end  of  the 
transmission  line  is  open-circuited  as  when  connected  to 
the  full  load,  because  of  the  breakdown  of  the  air  near  the 
conductors. 


252 


TRACTION  AND   TRANSMISSION. 


83.  Lightning.  —  The  physical  processes,  accompanying 
the  establishment  of  atmospheric  differences  of  potential, 
resultant  discharges  from  which  are  known  as  lightning,  are 
not  well  understood.  Closely  related  to  the  phenomenon 
are  two  facts  established  by  somewhat  recent  experiments. 

As  the  result  of  the  presence  in  the  earth  of  radioactive 
substances  and  the  characteristics  of  their  decay,  the  lower 


200 


150 


CO 

>100 


50 


10  20  30  40 

ELEVATION  IN  THOUSAND  FEET 

Fig.  103. 


50 


60 


strata  of  the  atmosphere  are  partially  ionized.  The  num- 
ber of  positive  ions  per  unit  volume  usually  exceeds  the 
number  of  negative  ions.  This  excess  seems  to  disap- 
pear at  an  elevation  of  about  10  miles.  The  resultant  posi- 
tive volume  electrification  establishes  a  positive  potential 
in  the  various  strata  with  respect  to  the  surface  of  the 
earth.  Fig.  103,  due  to  Liebenon,  shows  the  calculated 
potential  differences  for  strata  of  various  altitudes,  and  is 
based  upon  experimental  evidence. 

Air  saturated  with  water  vapor  requires  the  presence  of 


TRANSMISSION  LINES.  253 

solid  nuclei  in  order  that  the  vapor  may  condense  to  form 
the  globules  which  constitute  a  cloud.  Frequently  these 
nuclei  consist  of  dust  particles.  Kelvin  showed  that  the 
necessity  of  a  nucleus  was  due  to  the  influence  of  curvature 
of  surface  upon  the  vapor  tension,  because  the  greater  the 
curvature  of  a  liquid  surface  the  more  it  tends  to  evaporate. 
J.  J.  Thomson  showed  that  electrification  would  partially 
neutralize  the  effect  of  curvature;  and  C.  T.  R.  Wilson 
showed  that,  ionized  air  required  less  supersaturation  to 
effect  cloud  formation  than  non-ionized  air  and  that  nega- 
tive ions  were  more  effective  than  positive  ions.  Since 
uncharged  globules  of  a  cloud  continually  move  under  the 
influence  of  the  excess  of  gravitational  force  above  the 
force  of  air  resistance,  and  since  charged  globules  move  as 
the  result  of  an  additional  force  due  to  the  presence  of 
the  electric  field,  —  positive  or  negative  according  to  the 
sign  of  the  charge,  —  it  is  reasonable  to  believe  that  these 
forces  contribute  towards  the  establishment  of  potential 
differences  between  different  parts  of  a  cloud,  between 
clouds,  and  between  a  cloud  and  the  earth.  Under  poten- 
tial differences  of  sufficient  magnitude  the  intervening  air 
breaks  down  accompanied  by  a  discharge. 

The  gradual  formation  of  a  cloud  over  a  transmission  line 
electrostatically  induces  a  charge  in  the  line  wires  and 
holds  it  bound.  Upon  the  neutralization  of  the  cloud 
potential  by  discharge,  the  energy  of  the  charge  on  the 
lines  is  delivered  to  the  line,  and  tends  to  dissipate  itself 
under  conditions  prescribed  by  the  constants  of  the  line 
and  its  environment.  Current  surges  may  be  set  up  in  the 
line  circuit  and  be  superposed  upon  the  normal  currents, 
which  surges  will  cease  when  the  energy  has  been  expended 
in  heating  the  conductors,  or  an  arc  may  be  initiated 


254  TRACTION   AND   TRANSMISSION. 

between  a  wire  and  ground  over  an  insulator  or  between 
two  wires.  The  subsequent  maintenance  of  the  arc  will 
be  due  to  energy  supplied  by  the  generator.  The  current 
in  an  arc  to  ground  is  generally  intermittent  and,  if  main- 
tained, may  set  up  resonant  currents  in  apparatus  con- 
nected with  the  line,  since  each  piece  of  apparatus  has  a 
natural  frequency  of  its  own.  These  resonant  currents  are 
likely  to  be  accompanied  by  voltages  of  magnitude  suffi- 
cient to  destroy  insulation  and  cause  short  circuits. 

The  energy  of  the  magnetic  field  associated  with  a  short 
circuit  between  line  wires  is  delivered  to  the  line  when  the 
short  circuit  ceases,  and  may  cause  surges  similar  to  those 
which  result  from  lightning.  Some  writers  have  therefore 
extended  the  meaning  of  the  term  "  lightning  "  to  include 
such  phenomena. 


Fig.  104. 


84.  Protection  from  Lightning.  —  In  order  to  protect 
apparatus  from  the  high  voltages  due  to  lightning  it  is 
common  to  insert  choke  coils,  Fig.  104,  in  series  between  the 
apparatus  terminals  and  the  line  wires  so  that  the  incoming 


TRANSMISSION  LINES. 


255 


1 


high-voltage  wave  front  may  be  retarded  thereby  for  a 
short  interval  of  time.  On  the  line  side  of  the  choke  coil 
is  installed  a  grounded  device  which  conductively  connects 
the  line  with  the  ground  whenever  the  voltage  of  the  line 
exceeds  a  predetermined  value.  This  device  is  termed  a 
lightning  arrester,  and  its  operation,  in  connection  with  the 
choke  coil,  quickly  relieves  the  line  of  excessive  potentials. 
Some  means  must  be  employed,  however,  to  prevent  the 
maintenance  of  a  discharge  at  normal  voltage  from  the  line 
to  ground  over  the  path  rendered  conductive  by  the  initial 
discharge  under  excessive  potentials.  In  nearly  all  types 
of  arresters  the  circuit  from  the 
line  wire  to  the  ground  is  nor- 
mally interrupted  by  a  short 
dielectric  gap  which  will  break 
down  under  a  slight  excess  over 
normal  voltage.  The  various 
arresters  differ  from  each  other 
in  the  means  employed  to  sup- 
press the  subsequent  flow  of 
current  at  normal  voltage.  In 
one  type  this  is  accomplished 
by  separating  the  spark-gap 
electrodes  by  means  of  a  plunger 
solenoid;  in  another  there  is  an 
electromagnetic  blow-out;  and 
in  another,  for  use  on  alternat- 
ing circuits,  there  is  a  series  of 
gaps  between  electrodes  made 
of  metal  which  will  not  permit  the  maintenance  of  an  arc  at 
normal  potentials.  Another  type,  which  has  proved  effective 
in  the  protection  of  station  apparatus  on  alternating-current 


Fig.  105. 


256 


TRACTION   AND  TRANSMISSION. 


systems,  consists  of  a  series  of  aluminum  electrodes  upon 
whose  surfaces  are  formed  films  of  aluminum  hydroxide,  im- 
mersed at  short  distances  from  each  other  in  a  suitable  elec- 
trolyte. The  cross  section  of  such  an  arrester  is  shown  in  Fig. 
105,  and  is  characterized  by  the  conduction  of  very  minute 
currents  at  normal  voltage  and  of  very  large  currents, 
without  much  elevation  of  temperature,  at  voltages  slightly 
in  excess  of  normal. 

No  effective  means  has  been  found  for  the  protection  of 
a  transmission  line  from  a  direct  stroke  of  lightning.  Such 
strokes  usually  result  in  short  circuits  and  shattered  insu- 
lators. The  damage  is  usually  confined  to  one  tower  on 
metal  tower  lines,  but  extends  over  several  poles  when  the 
cross  arms  and  poles  are  of  wood. 

When  the  stroke  is  not  direct  but  in  the  vicinity  of  the 
line,  a  common  result  is  a  spill-over  or  arc  to  ground  over 


A 

B 

C                                              _/•> 

1  

in 

e±b 

OIL 
SWITCH 

I 

SELECTIVE!                    1   ^ 

RELAY     | 

1  '  1 

Fig.  106. 

an  insulator.  The  maintenance  of  the  arc  after  the  stroke 
by  energy  from  the  generator  is  likely  to  destroy  the  insu- 
lator, to  set  up  surges,  and  to  interrupt  the  service.  To 
interrupt  such  arcs,  E.  E.  F.  Creighton  has  devised  a  sup- 
pressor, which  automatically  grounds  the  affected  line  at 
the  station  for  a  short  interval  of  time,  sufficient  to  allow 


TRANSMISSION  LINES.  257 

the  conducting  vapors  to  escape  and  the  insulator  to  cool 
off.  This  time  is  not  so  great  as  to  interrupt  the  service 
because  of  the  slowing  down  of  synchronous  apparatus. 
The  arc  ceases  because  the  ground  at  the  station  robs  it  of 
its  potential.  Fig.  106  is  a  diagram  of  the  circuit  connec- 
tions. The  selective  relay,  which  controls  the  operation  of 
the  grounding  oil  switch,  is  itself  controlled  by  electro- 
static forces  on  high-voltage  lines  and  by  electromagnetic 
forces  on-, moderate-voltage  lines.  The  relay  contact  is 
normally  held  open  by  these  balanced  forces,  but  is  closed 
when  the  balance  is  destroyed. 

Efforts  have  been  made  to  protect  lines  by  ground  wires 
erected  above  the  line  and  connected  with  the  ground  at 
every  fifth  pole  or  so.  The  use  of  such  wires  has  resulted 
in  a  reduction  of  50  per  cent  in  insulator  failures.  Ground 
wires  but  partially  screen  the  line  wires  from  electrostatic 
induction  from  cloud  charges;  and  electromagnetic  induc- 
tion, accompanying  the  currents  which  follow  cloud  dis- 
charges, may  yield  high  voltages  in  the  line  wires. 

PROBLEMS. 

42.  Plot  a  curve  showing  the  resonant  frequency  of  open-circuited  trans- 
mission lines  of  various  lengths  when  connected  to  impedanceless  generating 
units.     What  length  of  line  corresponds  in  periodicity  with  the  fifth  har- 
monic of  a  wave  whose  fundamental  frequency  is  25  cycles? 

43.  Determine  the  economic  voltage  to  be  employed  in  transmitting 
15,000  kilowatts  at  25  cycles  to  a  single  substation  over  a  i2o-mile  three- 
phase  aerial  transmission  line  using  aluminum  conductors.     Take  the  equiv- 
alent annual  hours  of  operation  as  4000,  the  mean  annual  power  factor  as 
0.85,  the  cost  of  line  material  as  0.24  dollars  per  pound,  and  all  other 
factors  as  suggested  in  §  71. 

44.  What  is  the  size  and  what  must  be  the  separation  of  the  solid  con- 
ductors of  the  transmission  line  of  problem  43  for  the  avoidance  of  corona 
loss,  with  a  factor  of  safety  of  i.i  at  an  altitude  for  which  the  atmospheric 
pressure  is  700  mm.  Hg.,  and  at  a  temperature  of  30°  C. 


258  TRACTION  AND   TRANSMISSION. 

45.  Determine  the  line  constants  per  mile  per  phase  at  15°  C.  of  a  three- 
phase  6o-cycle  aerial  power  transmission  line  using  solid  hard-drawn  copper 
conductors  0.8  inch  in  diameter  spaced  triangularly  6  feet  apart. 

46.  Calculate  the  voltage  and  current  at  the  generator  end  of  the  line, 
the  efficiency  of  transmission,  the  voltage  regulation,  and  the  charging 
current  of  the  transmission  line  of  §  81  when  the  frequency  is  25  cycles,  all 
other  conditions  remaining  unaltered. 

47.  What  will  be  the  corona  loss  if  the  transmission  line  of  problem  46 
when  located  in  a  region  for  which  the  highest  temperature  is  30°  C.  and 
for  which  the    minimum  pressure  is  600   mm.,  is  open-circuited  at  the 
receiver? 


POWER   STATIONS. 


259 


CHAPTER  X. 

POWER    STATIONS. 

85.  Station  Load  Curves.  —  The  proper  design  of  a  power 
station  depends  to  a  large  extent  upon  the  characteristics 
of  its  output.  A  curve  with  ordinates  representing  the 
output  of  a  station  in  kilowatts  and  with  corresponding 


THOUSANDS  OF  KILOWATTS 
.  _  to  CO  -F> 

p^  o  o  o  c 

A 

L 

\ 

/ 

\ 

/ 

\ 

/ 

\ 

\ 

/ 

j 

\ 

/ 

V 

Z 

\ 

7 

\ 

\ 

/ 

\ 

^_ 

\ 

v.  

2 

2       2        4        6'       8        10      12        2        4        6        8        10      1S 
M,                                          TIME  IN  HOURS                                          P-N 

Fig.   107. 

abscissae  representing  the  time  of  day  is  termed  a  load 
curve  of  the  station.  Fig.  107  represents  a  typical  load 
curve  for  a  power  station  supplying  energy  for  traction 
purposes.  It  is  characterized  by  two  peaks,  which  occur 
at  about  8.30  in  the  morning  and  6.00  in  the  evening 
respectively,  and  which  last  for  two  or  three  hours,  and  by 


260  TRACTION  AND   TRANSMISSION. 

a  very  low  value  during  the  early  morning  hours.  The 
peaks  are  due  to  the  demands  of  traffic  in  carrying  pas- 
sengers to  business  in  the  morning  and  returning  them 
to  their  residences  at  night.  The  maximum  value  of  the 
peak  at  the  power  station  is  less  than  the  sum  of  the  peaks 
at  the  different  substations;  because  the  latter  occur  at 
different  times,  that  is,  because  of  the  diversity  factor.  In 
the  morning,  the  peaks  at  the  substations  in  the  residential 
districts  occur  prior  to  those  in  the  business  and  manu- 
facturing districts,  while  the  reverse  is  true  in  the  evening. 
Furthermore,  the  average  duration  of  the  power-station 
peaks  is  greater  than  characterizes  the  substation  peaks 
for  the  same  reason.  The  ordinates  of  the  load  curve  are 
greater  in  winter  than  in  summer  because  of  the  necessity 
for  heating  and  lighting  the  cars,  and  often  because  of  the 
presence  and  removal  of  snow.  The  energy  required  for 
heating  may  be  20  per  cent  of  that  required  for  car  propul- 
sion. The  shape  of  the  load  curve  is  likely  to  be  entirely 
different  on  Sundays  and  holidays  from  its  shape  on  week 
days  and  may  be  materially  modified  by  the  maintenance  of 
seasonal  amusement  or  recreation  resorts.  Instantaneous 
fluctuations  in  the  power  output,  not  shown  in  the  load 
curve  and  due  to  the  abnormal  currents  necessary  in  the 
starting  of  trains,  are  always  present.  With  few  cars  in 
operation  the  relative  magnitude  of  these  fluctuations  is 
greater  than  when  there  are  many.  The  amount  of  fluc- 
tuation can  be  determined  with  sufficient  exactitude  from 
the  curve  of  Fig.  58,  which  shows  the  dependence  of  the 
ratio  of  maximum  to  average  current  upon  the  number 
of  cars  in  operation. 

The  power-station  load  curve  for  a  proposed  installation 
can  be  predetermined  with  considerable  accuracy  from  the 


POWER   STATIONS.  261 

train-sheet,  §  52,  of  the  tentative  service  to  be  maintained 
and  the  curves  of  power  input  to  the  car,  §  43,  for  different 
times.  The  ordinate  of  a  point  on  the  power-station  load 
curve  for  a  given  instant  is  equal  to  the  sum  of  the  inputs 
to  all  cars  in  operation  at  that  instant,  divided  by  the 
product  of  the  efficiencies  of  transmission,  of  conversion, 
and  of  distribution,  which  product  usually  ranges  from 
70  per  cent  to  75  per  cent.  With  urban  systems,  where 
congestion  of  street  traffic  constantly  interferes  with  regu- 
larity of  schedules,  this  method  is  inapplicable.  In  such 
cases  a  fair  estimate  of  the  power-station  output  in  kilo- 
watts at  any  instant  is,  however,  numerically  one-half  the 
rated  horsepower  of  all  the  motors  on  cars  in  service  at  that 
instant.  This  method  of  estimation  is  based  upon  the  fact 
that  the  continuous  current  capacity  of  a  railway  motor 
is  about  one-half  its  capacity  when  nominally  rated  in  ac- 
cordance with  the  Standardization  Rules  of  A.I.E.E.  The 
average  power  supplied  to  a  certain  number  of  cars  is  there- 
fore one-half  the  rated  horsepower  of  the  corresponding 
motors,  and  with  an  efficiency  of  75  per  cent  in  transmission 
from  the  power  station  to  the  cars  a  kilowatt  at  the  station 
corresponds  to  a  horsepower  at  the  car. 

86.  Selection  of  Generators.  —  For  stations  of  small 
capacity  supplying  energy  for  short  roads  it  is  often  eco- 
nomical to  use  2  200- volt  generators,  as  the  cost  of  wiring  is 
less  than  for  lower  voltages  and  the  cost  of  insulation  is  less 
than  for  higher  voltages.  Furthermore,  this  being  a  stand- 
ard voltage  for  lighting  generators,  there  is  a  complete 
line  of  these  generators  available.  For  systems  where  the 
economic  voltage  for  transmission,  calculated  under  the 
assumed  use  of  step-up  transformers,  is  of  the  order  20 
kilovolts,  standard  generators  wound  for  12  kilovolts  and 


262  TRACTION  AND   TRANSMISSION. 

connected  directly  to  the  transmission  line  will  generally 
prove  more  economical.  For  transmitting  large  amounts 
of  power  at  higher  voltages  step-up  transformers  must  be 
used  while  the  generator  voltage  should  conform  with  stand- 
ards such  as  6.6  or  n  kilovolts. 

The  size  of  a  unit,  including  generator  and  prime  mover, 
should  be  such  as  to  entail  a  minimum  annual  charge  against 
it,  arising  from  its  cost  and  operation.  To  reduce  the 
relative  losses  in  a  unit  it  should  be  operated  as  nearly  as 
possible  at  that  load  which  gives  a  maximum  efficiency. 
Because  the  designed  operating  efficiency  is  generally  great- 
est at  about  rated  load  and,  because  of  the  characteristics 
of  the  load  curve,  the  losses  would  be  least  with  units  of 
minimum  rated  capacity.  The  efficient  use  of  such  small 
units,  however,  would  necessitate  frequent  starting  and 
stopping  of  the  different  units  corresponding  to  the  fluctu- 
ations of  load,  and  this  would  require  a  large  force  of 
attendants.  Furthermore,  the  cost,  the  deficiency,  and  the 
required  floor  space  per  kilowatt  is  greater  for  small  units 
than  for  large  ones,  and  therefore  the  proper  selection  is, 
by  nature,  a  compromise. 

Very  small  stations  are  generally  located  upon  cheap 
land  and  space  economy  is  of  no  great  importance,  whereas 
the  number  of  attendants  must  be  reduced  to  a  minimum. 
Furthermore,  the  cost  per  kilowatt  varies  so  greatly  with 
the  capacity  of  small  units  that,  if  capital  is  limited,  it  may 
be  necessary  to  install  but  a  single  unit.  For  the  sake  of 
reliability  of  service,  however,  it  is  undesirable  to  use  less 
than  two  units. 

For  the  average  station  of  moderate  capacity  four  units, 
one  of  which  serves  as  a  reserve  unit,  to  be  used  in  case  of 
failure  of  another,  will  generally  prove  most  economical. 


POWER   STATIONS.  263 

The  relative  values  of  the  early  morning  and  noonday 
loads,  which  endure  for  protracted  periods,  may,  however, 
make  it  desirable  to  use  a  larger  number  of  units  so  as  to 
operate  at  good  efficiency  during  these  hours. 

Very  large  stations  have  been  installed  in  the  past  with 
the  number  of  units  prescribed  by  the  maximum  capacity 
available.  Steam-turbine  units  are  now  constructed  which 
have  a  rated  capacity  of  20,000  kilowatts. 

According  to  the  standardization  rules  of  A.I.E.E.  gen- 
erators should  be  able  to  carry  a  25  per  cent  overload  for 
two  hours.  If  a  railway  power  station  were  to  be  equipped 
with  five  units,  each  of  rated  capacity  equal  to  one-fifth 
the  maximum  station  load,  then  in  case  one  should  fail 
the  whole  load  could  safely  be  carried  by  the  remaining 
four.  This  is  possible  because  the  fifth  unit  is  seldom  in 
service  for  more  than  two  hours  during'  the  peak  loads.  A 
reserve  unit  may  thus  be  dispensed  with.  If  the  power 
factor  of  the  load  on  the  generators  be  less  than  unity,  the 
overload  capacity  may  not  be  sufficient  as  a  substitute  for 
the  reserve  unit. 

87.  Types  of  Prime  Movers.  —  The  types  of  prime 
movers  at  present  available  for  electric  power  stations 
are  steam  engines,  internal  combustion  engines,  and  water 
wheels.  As  a  rule  that  type  should  be  employed  which 
will  result  in  a  minimum  average  cost  of  reliably  delivering 
a  kilowatt-hour  of  energy.  To  make  an  equable  com- 
parison the  point  of  delivery  should  be  the  same  in  all 
cases.  This  will  generally  require  for  hydraulic  plants  that 
a  part  or  the  whole  of  the  expense  of  the  transmission  sys- 
tem shall  be  considered  as  chargeable  to  the  power  station. 
If  the  financial  hazard  associated  with  the  undertaking  be 
large  or  if  capital  be  limited,  it  may  be  necessary  to  reduce 


264  TRACTION  AND   TRANSMISSION. 

the  first  cost,  the  plant  thereafter  being  burdened  with  an 
excess  cost  of  energy  production. 

Internal  combustion  engines  burning  gas  or  liquid  fuel 
in  their  cylinders  have  a  high  thermodynamic  efficiency. 
The  high  pressures  developed  require  heavy  construction, 
the  high  temperatures  require  cooling  systems,  and  the 
intermittent  release  of  energy  requires  heavy  flywheels. 
They  therefore  cost  more  than  other  forms  of  prime  movers, 
and  depreciate  in  value  faster.  Furthermore,  gas  engines 
have  a  very  limited  overload  capacity.  Reliability  in  their 
operation  has  not  been  sufficiently  established  to  warrant 
the  recommendation  of  their  adoption  as  a  sole  source  of 
power  in  a  station  for  supplying  energy  for  railways.  Yet 
the  Milwaukee  and  Northern  road  as  well  as  the  Warren 
and  Jamestown  road  are  operated  solely  from  generators 
driven  by  gas  engines. 

88.  Power  Station  Costs.  —  The  annual  cost  of  operat- 
ing a  station  is  conveniently  divided  into  two  parts,  namely, 
fixed  charges  which  do  not  vary  with  or  depend  upon  the 
output  of  the  station  after  it  is  built  and  equipped,  and 
operating  expenses  which  vary  with  the  output.  The 
fixed  charges  usually  comprise  interest,  taxes,  insurance, 
rental,  depreciation,  and  obsolescence.  Sometimes  there  is 
apportioned  to  the  power  station  a  part  of  the  annual 
administration  costs,  including  office  rentals,  salaries,  and 
legal  expenses.  The  operating  expenses  comprise  labor  or 
attendance,  repairs  and  maintenance,  fuel,  water,  oil,  waste, 
and  other  supplies. 


STEAM   STATIONS.  265 

STEAM    STATIONS. 

89.  Engines  and  Turbines.  —  Steam-driven  prime  movers 
may  consist  of  reciprocating  engines  or  turbines,  operated 
with  or  without  exhaust  steam  condensers.  The  former  are 
usually  either  simple  or  compound  and  are  sometimes  clas- 
sified as  high-speed  or  low-speed,  although  there  is  "no 
sharp  dividing  line  in  this  respect.  A  speed  of  150  revolu- 
tions per  minute  may  be  assumed  as  the  usual  line  of 
division.  The  proper  selection  of  a  prime  mover  of  this 
type  is  based  upon  the  first  cost  of  the  prime  mover  and  of 
the  rest  of  the  equipment  entailed  by  its  use,  as  well  as 
upon  the  expenses  of  maintenance  and  operation.  Data 
concerning  steam  prime  movers  generally  include  pounds 
of  steam  consumed  per  indicated  horsepower-hour  or  per 
kilowatt-hour  of  output,  initial  and  back  pressures  of 
the  steam,  and  the  mechanical  efficiency  of  the  mover. 
The  steam  consumption  and  efficiency  vary  with  the  load, 
as  does  the  efficiency  of  a  generator.  With  assumed  con- 
ditions as  to  pressures  and  load,  the  pounds  of  steam  per 
kilowatt-hour  of  generator  output  is  to  be  found  by  dividing 
the  pounds  of  steam  consumed  per  indicated  horsepower- 
hour  by  0.746  times  the  product  of  the  generator  and 
prime-mover  efficiencies.  The  steam  consumption  of  re- 
ciprocating engines  increases  somewhat  with  use,  whereas 
that  of  turbines  remains  fairly  constant.  The  steam  con- 
sumption of  Curtis  turbines  decreases  about  one  percent  for 
each  increment  of  10  pounds  in  gauge  pressure  and  one 
pound  per  kilowatt-hour  per  inch  of  vacuum. 

At  a  given  pressure,  steam  having  the  minimum  tempera- 
ture consistent  with  its  remaining  in  the  form  of  a  vapor 
is  termed  saturated  steam,  and  a  reduction  of  its  tempera- 


266  TRACTION  AND   TRANSMISSION. 

ture  causes  condensation.  If  saturated  steam  be  removed 
from  contact  with  water,  its  temperature  may  be  raised 
above  that  of  the  water  from  which  it  was  produced.  It 
then  acts  like  an  imperfect  gas  and  is  termed  superheated 
steam.  The  rise  of  temperature  in  degrees  Fahrenheit  is 
a  measure  of  the  amount  of  superheat.  If  steam  rises 
from  a  surface  of  water  faster  than  about  three  feet  per 
second,  it  carries  water  with  it  in  the  form  of  spray,  and 
when  fine  spray  is  once  formed  in  steam  it  does  not  readily 
settle.  The  resultant  mixed  steam  is  termed  wet  steam. 
Superheated  steam,  if  homogeneous,  cannot  be  wet,  be- 
cause water  particles  would  of  necessity  be  evaporated 
under  the  influence  of  heat  derived  from  the  surrounding 
steam. 

The  cyclical  changes  in  the  temperature  of  cylinder  walls, 
accompanying  the  operation  of  reciprocating  engines,  causes 
cylinder  condensation  losses  of  heat  when  it  is  fed  with 
saturated  steam.  Such  losses  are  seldom  less  than  10  per 
cent  and  often  amount  to  40  per  cent  of  the  supplied  energy, 
and  may  be  materially  reduced  by  the  use  of  superheated 
steam.  The  presence  of  moisture  in  the  steam  passing 
through  a  turbine  occasions  a  wear  of  the  turbine  blades 
as  the  result  of  impact.  It  is  therefore  desirable  to  supply 
superheated  steam  to  reciprocating  engines  on  the  ground 
of  economy  and  to  turbines  on  the  ground  of  maintenance. 
A  device  used  to  elevate  the  temperature  of  steam  above 
its  saturation  temperature  is  termed  a  superheater  and 
may  consist  of  a  set  of  tubes  connected  in  the  steam  line 
and  subjected  to  the  heat  from  the  fire  of  the  main  boiler 
or  from  an  auxiliary  source. 

The  data  contained  in  the  following  table  give  an  idea 
of  what  may  be  expected  as  to  the  performance  of  these 


STEAM   STATIONS.  267 

types  of  prime  movers.  The  efficiency  of  reciprocating 
engines  and  of  generators  has  been  assumed  as  92  per  cent 
and  97  per  cent  respectively. 

STEAM  CONSUMPTION. 


Type  of  engine. 

Pounds  of  steam 
per  K.W.H. 

SATURATED  STEAM: 
Simple  noncondensing  
Compound  noncondensing  

55 
35 

Simple  condensing  

33 

Compound  condensing 

27 

Turbines 

20 

SUPERHEATED  STEAM: 
Compound  condensing  
Turbines                         

14 
15 

90.  Condensers.  —  Consider  a  simple  engine  run  so  that 
the  steam  after  expansion  exhausts  into  the  atmosphere; 
that  is,  run  noncondensing.  The  effective  force  per  unit 
area  of  piston,  available  at  any  instant  for  performing 
work,  is  the  difference  between  the  pressure  of  the  steam 
on  one  of  its  surfaces  and  the  back  pressure  exerted  by  the 
atmosphere  at  that  instant  on  the  other  surface.  Since  the 
mean  effective  value  of  the  former  may  be  of  the  order 
50  lb./in.2  and  the  latter  is  14.7  lb./in.2,  a  reduction  of  the 
latter  to  1.7  would  theoretically  increase  the  power  out- 
put 13/50  or  26  per  cent.  An  enclosed  device  which  is 
adapted  to  receive  the  exhaust  steam,  lower  its  tempera- 
ture, and  thereby  condense  it,  is  termed  a  condenser.  Its 
use  materially  reduces  the  back  pressure  because  steam, 
after  condensation,  occupies  an  insignificant  portion  (ryV^) 
of  the  space  filled  by  it  prior  to  condensation.  In  order 
to  cool  and  condense  the  steam  it  must  be  deprived  of 


268  TRACTION  AND   TRANSMISSION. 

some  of  the  heat  associated  with  it.  This  may  be  done 
by  passing  it  along  one  surface  of  a  thin  metal  which  is 
kept  cool  by  water  circulated  in  contact  with  the  other 
surface  or  by  mixing  the  steam  with  a  spray  of  cooling 
water.  A  device  using  the  first  method  is  termed  a  sur- 
face condenser,  and  one  using  the  latter  is  termed  a  jet 
condenser.  The  condensing  water  used  with  the  jet  con- 
denser is  variously  termed,  as  injection,  cooling,  or  circulat- 
ing water.  To  maintain  the  condenser  in  operation  the 
condensed  water,  which  has  collected  in  a  hot  well,  must  be 
removed  by  a  wet-vacuum  pump,  which  may  also  serve  to 
remove  the  air  which  is  invariably  present  as  the  result  of 
leakage,  or  absorption  in  the  injection  water.  To  main- 
tain a  high  vacuum  an  additional  dry-vacuum  pump  is  often 
used  for  removing  the  air. 

The  amount  of  cooling  water  required  per  pound  of 
condensed  steam  depends  upon  the  vacuum  and  upon  the 
initial  and  final  temperatures  of  the  cooling  water. 

Let   X  =  total  heat  of  the  exhaust  steam  above  32°  F., 
T0  =  initial  temperature  of  the  cooling  water, 
T    _  ( temperature  of  the  condensed  steam  (surface), 

f  temperature  of  the  discharge  water  (jet), 
TZ  =  temperature  of  the  discharge  water. 

Then  the  weight  of  cooling  water,  W,  necessary  to  con- 
dense one  pound  of  saturated  steam,  is 

Tjr      X  -  Tl  +  32 

W  =  *T^   pounds. 

<L2   —    1  0 

Surface  condensers  cost  more  than  jet  condensers,  but 
permit  the  use  of  the  condensed  steam  as  feed  water  for 
the  boilers  after  any  oil,  which  became  mixed  with  it  in 
the  engine,  has  been  removed  from  it.  They  are  there- 


STEAM   STATIONS. 


269 


fore  adapted  for  use  where  there  is  a  limited  supply  of 
suitable  feed  water  but  a  superabundance  of  cooling  water, 
such  as  results  from  a  location  near  salt  waterways. 
When  the  supply  of  cooling  water  is  limited  the  use  of 
cooling  ponds  or  cooling  towers  permits  of  the  repeated  use 
of  the  same  water,  but  these  arrangements  are  expensive. 

The  advisability  of  installing  condensers  depends  upon 
whether  the  annual  saving  of  energy  is  greater  or  less  than 
the  annual  expense  entailed 
by  their  cost,  maintenance, 
and  operation. 

A  jet  condenser  is  shown 
in  Fig.  1 08  with  parts  cut 
away  so  as  to  indicate  the  in- 
terior construction.  The  ex- 
haust steam  enters  through 
the  large  pipe  at  the  left  and 
the  cooling  water  through 
the  large  pipe  at  the  right. 
The  latter  is  sprayed  through 
the  valve  in  the  center, 
mixes  with  the  steam,  con- 
denses it,  and  both  fall  into 
the  pipe  below.  The  air- 
pump  is  connected  with  the 
small  pipe  at  the  left.  With 
the  surface  condenser  shown  in  Fig.  109,  the  cooling  water 
is  passed  through  the  interior  of  the  small  tubes  and  ab- 
stracts heat  from  the  exhaust  steam,  which  surrounds  the 
tubes,  thereby  condensing  it.  The  circulating  pump  to 
the  right  and  the  vacuum  pump  to  the  left  are  operated 
by  an  intermediate  auxiliary  engine. 


Fig.  108. 


270 


TRACTION   AND   TRANSMISSION. 


91.  Boilers.  — An  essential  element  in  a  steam  plant  is 
the  boiler  equipment,  and  its  size  and  cost  depend  upon 
the  amount  of  steam  which  is  to  be  supplied  to  the  prime 
movers  and  to  the  auxiliaries.  A  typical  form  of  boiler  for 
use  in  power  stations  is  shown  in  Fig.  no,  wherein  the  water 
to  be  heated  circulates  as  the  result  of  localized  tempera- 
ture differences,  moving  to  the  right  in  the  cylindrical 


I/ 


=!•• 


Fig.  109. 

drum  at  the  top,  and  to  the  left  in  the  water  tubes,  which  are 
enveloped  in  the  hot  gases  resulting  from  the  combustion 
of  the  fuel.  These  gases  ultimately  pass  through  the 
damper-controlled  opening  near  the  top  of  the  right-hand 
enclosing  brick  wall,  and  through  a  breeching  to  the  chimney 
or  stack.  Steam  is  generated  and  confined  under  pressure 
in  the  upper  part  of  the  drum,  and  is  fed  through  the  nozzle 
on  top  to  a  header,  whence  it  is  conducted  direct  to  the  prime 
mover.  The  capacity  of  a  boiler  is  rated  in  horsepower 


STEAM   STATIONS.  271 

and  the  builder's  rating  is  based  upon  a  heating  surface  of 
10  to  12  square  feet  per  horsepower.  A  boiler  of  one 
horsepower  capacity  is  considered  to  be  capable  of  allowing 
an  evaporation  of  34.5  pounds  per  hour  of  water  at  212°  F. 
into  steam  at  atmospheric  pressure,  and  to  have  an  over- 
load capacity  of  33^  per  cent.  If  the  temperature,  /,  of 
the  feed  water  be  less  than  212°,  the  steam  be  x  part  dry, 
or  the  steam  be  superheated  t°  F.,  the  delivery  of  34.5 


Fig.  no. 


pounds  of  steam  per  hour  under  such  conditions  will  re- 
quire a  boiler  of  more  than  unit  capacity,  and  to  deliver  Q 
pounds  of  steam  per  hour  the  horsepower  capacity  of  the 
boiler  should  be 


\  h 
/ 


34-5  970-4 

where   r  =  latent    heat   of   evaporation   at   the   resultant 

pressure, 

q  =  heat  in  liquid  at  this  pressure,  and 
C  =  mean  specific  heat  of  the  superheated  sf  earn. 


272  TRACTION  AND   TRANSMISSION. 

The  values   of   the  various   constants  may  be   found  in 
Engineering  handbooks. 

The  steam  consumed  in  operating  auxiliaries  such  as 
feed  pumps,  vacuum  pumps,  and  circulating  pumps,  ranges 
from  6  per  cent  to  15  per  cent  of  that  taken  by  the  prime 
movers.  Available  boilers  are  limited  in  capacity  to  about 
2250  horsepower,  and  it  is  common  to  install  smaller  ones 
in  batteries  of  two  or  more. 

92.  Feed-water  Heaters.  —  It  is  undesirable  to  pump 
cold  water  into  a  hot  boiler  because  of  excessive  stresses 
which  may  result  from  wide  differences  in  the  temperature 
of  adjacent  parts  of  the  metal  of  the  boiler.     Furthermore, 
there  is  a  saving  of  about  one  per  cent  in  fuel  for  every 
ii  degrees  elevation  in  the  temperature  of  the  feed  water, 
provided  such  elevation  is  produced  by  heat  that  would 
otherwise  be  lost.     The  temperature  of  the  feed  water  may 
be  raised   by  heat  taken  from  the  exhaust  steam  through 
the  aid  of  a  vacuum  heater  or  an  atmospheric  heater,  and  by 
heat  from  the  hot  flue  gases,  using  an  economizer. 

93.  Chimneys  or  Stacks. — A  chimney  serves  two  pur- 
poses, namely,  to  carry  off  the  obnoxious  gases  resulting 
from  combustion,  and  to  produce  a  draft  which  will  give  a 
sufficient  supply  of  oxygen  for  combustion.     The  former 
requires  an  adequate  cross  section  and  the  latter  an  ade- 
quate height  of  chimney.     Experience  shows  that  the  draft 
pressure,  measured  in  inches  of  water  as  compared  with 
atmospheric  pressure,  should  be  from  0.5  to  1.5  inches,  de- 
pending upon  the  character  and  size  of  the  fuel  to  be  used, 
and  upon  the  quantity  to  be  burned  per  square  foot  of  grate 
surface.     Heights  above  the  grate,  which  have  given  satis- 
factory results  in  practice  with  plants  of  moderate  capacity 
employing  different  fuels,  are  given  in  the  following  table: 


STEAM    STATIONS.  273 

HEIGHTS  OF  CHIMNEYS. 


Fuel. 

Height  in  feet. 

Free-burning  bituminous 

80 

Anthracite   large  sizes 

IOO 

Slow-burning  bituminous            

1  20 

Anthracite  buckwheat      

I  iCO 

Anthracite  slack              

175 

The  ascending  gases  in  a  chimney  are  retarded  by  fric- 
tion in  the  vi'cinity  of  the  walls,  and  the  equivalent  cross 
section  A  of  a  round  chimney  is  therefore  generally  taken 
as  that  corresponding  to  a  diameter  four  inches  less  than 
the  real  internal  diameter  of  the  chimney.  Assuming  a 
coal  consumption  of  five  pounds  per  horsepower-hour, 
a  chimney  of  height  h  feet,  properly  to  carry  off  the  gases 
from  boilers  of  P  horsepower,  should  have  an  equivalent 
cross  section  of 

°-3^  f 

A  =       -  square  feet. 

Vh 

Chimneys  are  constructed  of  steel,  reenforced  concrete, 
or  masonry.  Steel  chimneys  weigh  less,  cost  less,  require 
less  space,  expose  less  surface  to  the  wind  than  other  forms, 
and  are  more  efficient  because  they  are  air-tight.  They, 
however,  depreciate  more  rapidly  because  of  rust  and  be- 
cause of  the  corrosive  influence  of  the  flue  gases. 

Sometimes  short  chimneys  are  used  in  connection  with 
mechanical  draft  apparatus,  consisting  of  either  an  exhaust 
fan  in  the  smoke  flue  or  a  mechanical  or  steam-jet  blower 
underneath  the  grate  bars.  An  induced  draft  is  produced 
by  the  former  and  a  forced  draft  by  the  latter.  The  advis- 
ability of  installing  mechanical  draft  apparatus  is  depend- 
ent upon  the  results  of  an  economical  comparison  with 


274 


TRACTION  AND   TRANSMISSION. 


the  saving  resulting  from  the  lessened  necessary  height  of 
chimney. 

94.  Buildings.  —  Power-station  buildings  may  be  con- 
structed of  wood,  brick,  reenforced  concrete,  or  stone. 
Wood  is  used  only  for  very  small  stations  and  stone  only 
for  elaborate  stations.  If  a  single  building  is  used  for 
housing  the  boiler  plant  as  well  as  the  generating  plant,  the 

4 


£s 

cc 

LJ 
Q. 


OC 

li 


o  cu 


?TIS  TURBINES. 


X  RECIPROCATING  ENGINES 


10       20      30     40      50      60      70      00      90    100 
THOUSANDS  OF  KILOWATTS 

Fig.  in. 

two  should  be  separated  by  a  brick  wall  with  no  openings 
in  it  which  will  allow  dirt  to  pass  through  from  the  boiler 
room  to  the  engine  room.  The  boilers  and  the  units  which 
are  supplied  with  steam  from  them  should  be  on  opposite 
sides  of  the  dividing  wall  and  so  placed  as  to  reduce  the 
length  of  steam  piping  to  a  minimum.  The  height  of  both 
rooms  should  be  ample,  to  permit  the  use  of  lifting  machinery 
and  the  replacing  and  repairing  of  boilers.  The  building 
should  be  well  lighted,  well  ventilated,  of  fire-proof  con- 
struction, and  arranged  with  a  view  to  extension  in  case  of 
growth  of  demanded  output. 


STEAM   STATIONS.  275 

The  floor  space  required  for  turbines  is  materially  less 
than  that  for  reciprocating  engines  of  the  same  capacity  and 
the  foundations  can  be  much  lighter.  Where  the  cost  of 
land  is  great  a  considerable  saving  may  be  effected  by  placing 
turbines  on  a  floor  above  the  boiler  room.  The  station  is 
then  termed  a  double-deck  station.  The  space  required  for 
passageway  around  units  is  greater  per  kilowatt  for  small 
units  than  for  large  ones.  The  curve  of  Fig.  1 1 1  is  based  upon 
existing  plants,  and  shows  the  average  floor  space  allowed 
per  rated  kilowatt  in  terms  of  the  total  capacity  of  a  plant. 

95.  Arrangement  of  Apparatus.  —  It  is  customary  to 
arrange  the  apparatus  in  a  steam-power  station  so  that  the 
path  of  energy  is  as  short  as  possible.  The  coal  is  there- 
fore received  and  delivered  to  the  boilers  at  one  end  of  the 
station  and  the  electrical  energy  is  delivered  to  the  line 
from  the  generators  at  the  other  end.  Figs.  112  and  113 
show  an  elevation  and  floor  plan  of  the  Winona  Interurban 
Railway  Power  House  which  has  a  capacity  of  1200  K.W. 
The  output  is  supplied  at  33,000  volts  from  two  banks  of 
three  transformers,  each  of  200  K.W.  capacity  and  stepping 
the  voltage  up  from  2300  volts.  There  are  two  6oo-K.W. 
25-cycle,  2300- volt  generators,  each  directly  connected  to  a 
cross-compound  engine  guaranteed  to  have  a  full-load 
steam  consumption  not  to  exceed  14.1  pounds  per  indicated 
horsepower-hour  at  140  pounds  pressure  and  26  inches  of 
vacuum.  Each  engine  is  supplied  with  a  jet  condenser. 
Steam  is  supplied  by  four  boilers,  arranged  in  batteries  of 
two  each,  there  being  3000  square  feet  of  heating  surface 
provided  in  each  unit.  It  will  be  noted  that  a  transformer- 
converter  substation,  for  supplying  600- volt  direct  current 
to  the  distribution  circuits  in  the  immediate  vicinity  is 
housed  under  the  same  roof. 


TRACTION  AND   TRANSMISSION. 


STEAM   STATIONS. 


277 


Fig.  114  shows  a  cross  section  of  the  Port  Morris  Power 
House  of  the  New  York  Central  Railroad,  which  is  equipped 
with  Curtis  steam-turbine  units  and  surface  condensers. 


Fig.  113. 


The  very  complete  system  of  labor-saving  apparatus  for 
conveying  coal  and  removing  ashes  and  its  method  of 
operation  is  clearly  shown. 


278 


TRACTION   AND  TRANSMISSION. 


STEAM   STATIONS. 


279 


POWER-PLANT   COSTS  PER  KILOWATT. 


Min. 

Max. 

i     Real  estate                                               

$3-00 
•75 

2.00 
•50 

8.00 
8.00 
i-5o 
i  .40 
.70 
i  .20 
.40 

2.OO 

15 
.40 

•50 
I-25 
9-50 
1-25 
1.30 
1.30 
.60 

1-25 
.40 
.20 
3.00 
.60 
.60 
22.OO 
.40 
I  .OO 

6.00 
16.00 
.60 
22.00 
.60 
3.00 
.20 
•IS 

.20 

I-2S 
2.OO 
4.00 

$7-00 
1-25 

3-00 

•75 

IO.OO 
IO.OO 

2.50 
2.80 
1-50 

2.OO 

.60 
2.75 
•  30 

1  .00 

I.  00 
2.OO 
II  .50 

i-75 

2.  2O 
2-25 
.90 
1.65 

•75 
•35 
5.00 
i  .00 
i  .00 
30.00 
.70 
2.50 
7-50 
22.00 
.80 
32.00 
i  .00 
3-9° 
•30 
•35 

•30 
1-75 

2.00 

6.00 

2     Excavation                                         

3     Foundations,  reciprocating  engines  

4.    Foundations,  turbines   

5.    Iron  and  steel  structure  

6     Building  (roof  and  main  floor) 

7     Galleries    floors  and  platforms                

8     Tunnels,  intake  and  discharge  

9.    Ash  storage"  pocket                  

10.    Coal  hoisting  tower       

n.    Cranes                              

12     Coal  and  ash  conveyors 

13     Ash  cars   locomotives   and  tracks 

14     Coal  and  ash  chute^                                        .... 

15.    Water  meters,  storage  tanks,  and  mains  
16.    Stacks                             

17.    Boilers                         

18.    Boiler  setting       

jo     Stokers 

20     Economizers 

21     Flues   dampers   and  regulators 

22     Forced  draft  blowers,  air  ducts             

23     Boiler,  feed,  and  other  pumps           

24.    Feed-water  heaters.                 

25.    Piping,  traps,  and  separators  

26     Pipe  covering 

27     Valves 

28     iMain  engines   reciprocating 

29     Exciter  engines  reciprocating.                 

30.    Condensers  barometric  or  jet         

31.    Condensers,  surface                  

32     Electric  generators 

33     Exciters 

34     Steam-turbine  units   complete 

35     Converters   transformers   blowers 

36     Switchboards   complete 

37.    Wiring  for  lights,  motors,  etc  
38.    Oiling  system                                 

39.    Compressed  air  system  and  other  small  aux- 
iliaries   

40     Painting   labor   etc 

41     Extras 

42.    Engineering  expenses  and  inspection  

280 


TRACTION  AND   TRANSMISSION. 


96.  Cost  of  Steam  Stations.  —  The  table  on  the  preced- 
ing page,  due  to  H.  G.  Stott,  includes  the  approximate 
cost  per  kilowatt  of  the  various  elements  entering  into  the 
cost  of  a  steam  plant.     A  fair  average  cost  per  kilowatt  is 
$100  for  plants  using  reciprocating  engines  and  $80  for 
those  using  steam-turbine  units. 

97.  Operating    Expenses.  —  Data    concerning    twenty- 
three  stations  of  moderate  capacity,  using  mostly  bitu- 
minous coal  ranging  in  price  from  $2.75  to  $5  per  gross 
ton,  and  all  operated  condensing,  has  been  published  re- 
cently by  E.  F.  Tweedy.     Fig.  115  shows  the  operating  costs 


COST  PER  KILOWATT  HOUR  GENERATED 
EXCLUSIVE  OF  FIXED  CHARGES- 
-  CENTS.  10  co 

x 

0  RECIPROCATING  STEAM  ENGINES. 
•  STEAM  TURBINES. 
XMIXED  EQUIPMENT-ENGINES  &  TURBINES, 
EQUATION  OF  HYPERBOLIC  CURVE 
y=1  +  900,000 

\ 

\    « 

\ 
\ 

O 

s 

c 

'bx^ 

^ 

x 

—  ^ 

>-°-K 

x 

x 

D 

x 

• 

1              23456789 
MILLIONS  OF  KILOWATT  HOURS  GENERATED  PER  YEAR. 

Fig.  n5. 

per  kilowatt-hour  in  terms  of  total  annual  outputs.  The 
highest  load  factor  based  upon  rated  capacity  was  0.23, 
the  lowest  o.u,  and  the  average  0.17.  The  coal  consumed 
per  kilo  watt- hour  ranged  from  a  little  over  3  pounds  for 
the  larger  plants  to  about  5  pounds  for  the  smaller  ones. 
The  station  rating  in  kilowatts  per  man  employed  in 
operating  the  station,  ranged  from  about  100  K.W.  for  the 


HYDRAULIC    STATIONS. 


28l 


smallest  stations  to  250  K.W.  for  the  largest.  Fig.  116 
shows  the  percentage  distribution  of  operating  costs  among 
fuel,  labor,  and  miscellaneous  items. 


12345678 
MILLIONS  OF  KILOWATT  HOURS  GENERATED  PER  YEAR. 

Fig.  116. 


HYDRAULIC    STATIONS. 

98.  Turbines.  —  In  procuring  mechanical  energy  from 
water  power  two  classes  of  turbines  or  water  wheels  may 
be  utilized  in  conformity  with  American  practice;  namely, 
the  reaction  turbine  and  the  impulse  wheel. 

The  reaction  or  pressure  turbine  of  the  mixed-flow  type 
is  applicable  for  low  and  moderate  heads,  say  up  to  150  feet, 
although  this  type  has  been  used  for  heads  up  to  600  feet. 
It  consists  of  a  rotating  wheel  or  runner  carrying  vanes  or 
buckets  to  which  water  under  pressure  is  delivered  radially 
inward  by  means  of  stationary  guide  vanes  surrounding  the 
wheel,  and  from  which  the  water  is  discharged  partially 
in  an  axial  and  partially  in  a  radial  direction.  Torque 
is  developed  by  reaction,  due  to  changing  the  direction  of 
water  flow. 


282  TRACTION  AND   TRANSMISSION. 

As  the  buckets  and  wheel  passages  are  always  completely 
filled  with  water,  it  is  not  necessary  to  mount  the  turbine 
at  the  Jevel  of  the  discharged  or  tail  water  in  order  to  realize 
the  total  head,  if  an  air-tight  draft  tube  leading  from  the 
.wheel  outlet  down  somewhat  below  the  level  of  tail  water 
be  provided;  for  the  falling  water  in  the  draft  tube  from 
the  turbine  creates  a  vacuum  that  is  effective  in  sucking 
the  water  through  the  turbine,  and  which  is  equivalent  to 
increasing  the  pressure  of  the  inflowing  water.  Reaction 
turbines  may  be  placed  at  any  level  up  to  about  20  feet 
above  the  tail  race  without  loss  of  head. 

The  power  developed  by  a  turbine  under  a  given  head 
is  regulated  by  varying  the  amount  of  water  admitted  to 
the  runner  by  means  of  gates.  There  are  various  types  of 
gates,  including  the  so-called  cylinder,  register,  and  wicket 
gates,  the  last  being  the  most  used.  In  this  type  the  guide 
vanes  are  pivoted  so  that  all  may  simultaneously  approach 
or  recede  from  their  neighbors  by  the  rotation  of  a  single 
regulating  shaft. 

In  order  to  neutralize  the  end  thrust  due  to  the  axial 
pressure  of  the  water,  as  well  as  to  secure  higher  speeds 
under  a  given  head,  it  is  common  to  place  two  turbine 
runners  —  of  correspondingly  reduced  diameter  for  the 
same  total  power  output  —  on  a  single  shaft.  Sometimes 
four  and  even  six  runners  are  coupled  together  to  constitute 
a  single  unit.  Fig.  117  shows  a  9000  horsepower  Allis- 
Chalmers  horizontal  twin  turbine  with  the  runners  dis- 
mantled. The  water  enters  through  the  wicket  gates  at 
the  ends  and  within  the  bearings,  passes  through  the  wheels, 
and  emerges  at  the  bottom. 

Impulse  wheels,  suitable  for  heads  above  150  feet,  com- 
prise a  number  of  buckets  into  which  water  is  directed 


HYDRAULIC   STATIONS. 


283 


284 


TRACTION  AND   TRANSMISSION. 


through  one  or  more  nozzles  at  a  velocity  equal  to  \/2  gH 
feet  per  second,  where  g  is  the  acceleration  due  to  gravity 
=  32  ft.  per  sec.  per  sec.,  and  H  is  the  head  or  height  of 
water  in  feet.  Each  bucket  forms  two  cups  divided  by  a 
central  ridge  which  separates  the  impinging  water  into  two 
parts,  each  part  being  deflected  backward  to  one  side  of  the 


Fig.  118. 

wheel  by  the  bucket.  The  effective  head  is  that  from  the 
level  of  headwater  to  the  nozzle,  the  head  from  the  latter 
to  the  tailwater  being  lost;  consequently  the  impulse  wheel 
should  be  placed  as  low  as  possible.  The  flow  of  water  is 
regulated  by  needle  valves  or  by  deflecting  the  nozzle. 
Fig.  118  shows  a  twin  Pel  ton  water  wheel  with  its  "  hy- 
draulic relay  "  governor. 

Governors  are  used  on  both  types  of  water  turbines  for 
automatically  effecting  the  opening  and  closing  of  the  regu- 


HYDRAULIC   STATIONS.  285 

lating  gates  or  for  deflecting  the  jet  from  the  buckets  of  im- 
pulse wheels.  As  the  force  required  for  this  purpose  is  very 
large,  it  is  evident  that  the  centrifugal  ball  governor  cannot 
directly  control  the  gate  opening,  but  must  do  so  through 
the  intervention  of  a  relay.  Two  general  types  of  relay  are 
used :  mechanical  relays,  which  derive  power  for  their  opera- 
tion from  the  water  wheel  by  means  of  gears,  pulleys,  or 
other  mechanical  devices,  and  hydraulic  relays,  which  are 
operated  either  by  the  pressure  of  water  taken  from  the 
"  penstock  "  or  other  source,  or  by  oil  supplied  under  high 
pressure  from  a  reservoir. 

Turbines  or  water  wheels  are  ordinarily  direct-connected 
to  the  electric  generators,  but  may  be  either  geared  or 
belted  thereto,  there  being  one  prime  mover  for  each  gen- 
erator, and  one  or  more  additional  turbines  for  the  exciter 
units.  Four  generator  units  is  considered  the  minimum 
number  allowable  for  the  attainment  of  a  reasonable  de- 
gree of  insurance  against  shut-down. 

Having  determined  the  number  and  size  of  the  electric 
generating  units  from  a  study  of  the  load  curves  on  the 
power  station,  the  size  of  the  prime  mover  in  horsepower  is 
found  by  dividing  the  kilowatt  rating  of  the  generator  by 
0.746  times  the  efficiencies  of  the  generator  and  mover.  The 
efficiency  of  large  generators  at  full  load  may  be  taken  as 
between  93  and  97  per  cent.  The  efficiency  of  turbines 
and  water  wheels  is  conventionally  taken  as  80  per  cent, 
although  efficiencies  as  high  as  86  per  cent  have  been 
attained.  Some  of  the  turbines  of  a  hydroelectric  power 
house  should  have  a  high  efficiency  at  low-gate  opening  and 
others  should  have  their  greatest  efficiency  at  full -gate,  so 
as  to  realize  a  fairly  high  all-day  plant  efficiency  under 
widely  varying  loads.  Representative  efficiency  curves  of 


286 


TRACTION  AND   TRANSMISSION. 


two  modern  reaction  turbines  at  various  gate  openings  are 
shown  in  Fig.  119. 

The  power  developed  by  a   turbine  or  impulse  wheel 
depends  upon  the  quantity  of  water  passing  through  it  in 


100 


60 


o 

tr 

£40 


20 


1/4  1/2  3/4 

GATE  OPENING 


FULL 


Fig.  119. 

unit  time,  upon  the  available  head  of  water,  and  upon  the 
turbine  efficiency,  e,  and  is 

D       62.4  qeH       qeH , 
P  =  -   — —  =  -  —  horsepower, 
550          8.81 

where  q  is  the  discharge  in  cubic  feet  per  second  and  which 
may  be  expressed  empirically  as 

q  =  KD2  VH, 

wherein  D  is  the  diameter  of  the  runner  in  feet,  and  K  is 
an  experimental  constant  of  discharge  dependent  upon  the 
design  of  the  turbine.  Therefore 

horsepower, 


8.81 


HYDRAULIC    STATIONS.  287 

whence  the  proper  wheel  diameter  for  a  given  head  is 

.81  P, 

-  feet.  (i) 


The  values  of  K  vary  widely  among  the  different  designs  of 
various  manufacturers,  but  most  values  thereof  lie  between 
2.3  and  3.5  for  reaction  turbines,  and  between  0.015  and 
0.024  for  impulse  wheels. 

For  a  given  turbine  the  speed  of  the  runner  varies  with 
the  square  ro'ot  of  the  head.  Let  r  be  the  rado  of  the 
peripheral  velocity  of  the  buckets  to  the  theoretical  velocity 
that  water  would  acquire  in  falling  freely  a  height  equal  to 
the  head  of  water.  Then  the  speed  of  the  wheel  in  revolu- 
tions per  minute  is 

T7     60  r  V2  gH  rH%  (  . 

=  IK-- 


The  values  of  r  range  from  0.65  to  0.93  with  different 
designs  of  reaction  turbines  and  between  0.43  to  0.51  with 
impulse  wheels.  Having  determined  the  turbine  speed  for 
a  given  head  of  water,  the  multipolarity  of  the  alternators 
for  the  generation  of  electromotive  forces  of  definite  fre- 
quency becomes  known. 

As  an  illustration  of  the  foregoing,  determine  the  proper 
number  of  poles  for  a  2000  K.W.,  6o-cycle,  three-phase 
alternator  which  is  to  be  driven  by  a  Pelton  water  wheel 
on  a  head  of  970  feet,  the  constants  of  the  wheel  being 
K  =  0.019,  r  =  0.505,  and  e  =  0.83.  Taking  the  alternator 
efficiency  as  92  per  cent,  the  rating  of  the  prime  mover  is 

=  3500  horsepower  and  the  diameter  of 


0.746  X  0.83  X  0.92 


the  water  wheel  is  J    S'Sl  X  3f°     =8.0  feet.     Therefore 
v  0.019  (970)^  0,84 


288  TRACTION  AND   TRANSMISSION. 

its  speed  is  H-  0.505  Vgyo  =  300  revolutions  per  minute. 
At  this  speed  there  must  be  24  poles  for  the  production  of 
6o-cycle  currents. 

99.  Water-power  Development.  —  In  any  hydraulic  de- 
velopment the  water  must  be  conducted  from  some  source 
to  the  wheels  by  means  of  a  head-race,  and  discharged 
from  the  turbines  into  the  tail-race  at  a  lower  level.  Two 
general  types  of  water-power  development  are  discernible 
which  usually  characterize  respectively  low-head  and  high- 
head  developments;  namely,  (i)  where  the  entire  head 
is  utilized  at  the  dam,  the  power  station  being  located  at 
one  end  thereof;  (2)  where  long  pipe  lines,  canals,  or  flumes 
are  required  to  transfer  the  water  from  the  intake  at  the 
headworks  to  the  station,  this  distance  being  only  suffi- 
ciently long  to  secure  for  a  given  amount  of  water  a  head 
which  will  enable  the  generation  of  the  required  power. 

(i)  The  object  of  a  dam  is  to  concentrate  the  fall  of  a 
stream  so  that  the  water  power  becomes  available  by  the 
elevation  of  the  water  surface.  That  portion  of  a  dam 
over  which  excess  water  pours  is  called  the  spillway,  and 
this  must  be  sufficiently  long  to  allow  escape  of  the  water 
in  times  of  heavy  flood  without  undue  rise  in  level  of  the 
water  in  the  reservoir  above  the  dam.  It  is  essential  that 
the  dam  have  a  solid  foundation,  that  it  be  stable  against 
overturning  and  be  water-tight,  and  that  it  be  so  con- 
structed as  to  prevent  washing  out  of  the  river  bed  and 
banks  below  it  and  erosion  of  the  dam  itself.  Dams  may 
be  constructed  of  timber,  masonry,  or  reenforced  concrete. 
They  must  be  equipped  with  drain  or  sluice  gates  for  the 
purpose  of  draining  the  reservoir  above  them  as  well  as  for 
assisting  in  the  discharge  of  water  during  the  heaviest 
floods.  The  surface  of  the  reservoir  may  be  raised  at 


HYDRAULIC   STATIONS. 


289 


times  by  means  of  flashboards,  which  collapse  automatically 
upon  excessive  rise  of  water. 

A  plan  of  a  typical  low-head  hydraulic  development  is 
illustrated  in  Fig.  120,  which  shows  the  Johnsonville  de- 
velopment of  the  Schenectady  Power  Company.  This  dam 
causes  the  flooding  of  850  acres,  thereby  giving  a  storage 


Fig.  lao. 

capacity  or  pondage  of  about  350  million  cubic  feet.  Fig. 
121  shows  the  power  house  and  sluice-gate  masonry  of  this 
development,  looking  upstream. 

The  power  furnished  by  a  given  stream  may  be  increased 
by  a  suitable  reservoir,  for  the  water  impounded  during  the 
rainy  seasons  may  be  partially  drawn  off  during  time  of  low 
water.  The  water  available  for  pondage  is  limited,  how- 
ever, since  the  level  of  head  water  can  only  be  lowered  a 
comparatively  small  amount  without  impairing  the  output 
and  efficiency  of  the  plant. 

Water  is  led  from  the  head-race  or  the  reservoir  through 


2QO 


TRACTION   AND    TRANSMISSION. 


suitable  hand-  or  motor-operated  head  gates  to  the  forebay 
and  from  there  to  the  wheel  pits.  The  water  in  entering 
the  wheel  pit  from  the  head-race  usually  passes  through  a 
trash  rack  consisting  of  narrow  iron  bars,  the  function  of 
which  is  to  prevent  large  floating  objects  from  entering  the 
turbines.  Open  wheel  pits  are  usual  for  heads  up  to  30 
feet,  whereas  closed  flumes  or  penstocks  leading  from  the 


Fig.  121. 


head-race  to  the  wheel  pits  are  utilized  for  higher  heads. 
It  is  desirable  to  set  the  turbines  in  separate  pits  so  that 
one  or  more  may  be  temporarily  shut  down  without  inter- 
fering with  the  operation  of  the  station. 

A  cross-sectional  view  of  the  Rocky  Creek  Power  House 
of  the  Southern  Power  Company  is  shown  in  Fig.  122,  which 
also  illustrates  the  construction  of  the  penstock  and  draft 
tube  for  each  turbine,  and  the  water-tight  stuffing  box 
between  the  wheel  pit  and  the  generator  room. 


HYDRAULIC   STATIONS. 


291 


Fig.  122. 


202 


TRACTION  AND   TRANSMISSION. 


Fig.  123  shows  the  interior  of  the  Rainbow  Station  of  the 
Great  Falls  Power  Company,  Montana.  Each  of  the  six 
3500  K.W.  alternators  is  driven  by  a  6000  H.P.  reaction 
turbine  with  two  runners,  each  runner  being  enclosed 
in  a  separate  spiral  casing  fed  by  a  separate  8-foot  steel 


Fig.  123. 

penstock  from  a  balancing  reservoir  and  discharging  into 
a  common  draft  tube. 

(2)  High-head  developments  require  long  canals  or  pipe 
lines  for  conveying  water  from  the  intake  to  the  power 
house.  Level  canals  may  be  constructed  along  the  hillside 
to  a  point  above  the  power  station,  and  from  there  the 
water  can  be  passed  down  to  the  water  wheels  through  a 


HYDRAULIC   STATIONS.  293 

penstock.  It  is  usually  cheaper,  however,  to  use  a  pipe 
line  which  need  not  be  level  but  can  follow  the  contour  of 
the  land.  Wood,  cast-iron,  or  riveted  wrought-iron  pipe  is 
used  for  such  purposes.  The  transmission  of  water  through 
pipes  or  canals  is  accompanied  by  a  reduction  in  the  avail- 
able head,  the  extent  of  which  depends  upon  the  size  of  the 
pipe  or  canal.  This  loss  of  head  can  be  computed  from 
expressions  given  in  most  books  on  Hydraulics. 

Provision  must  be  made  to  prevent  injury  to  penstocks 
or  pipe  lines  which  might  occur  when  the  turbine  gates  or 
water-wheel  nozzles  are  regulated  too  quickly.  Automatic 
relief  valves  of  sufficient  area  may  be  employed  at  the  lower 
end  of  the  pipe,  or  either  standpipes  or  surge  tanks  may  be 
used  to  alter  the  velocity  of  the  water  in  the  pipes. 

Fig.  1 24  gives  a  sectional  view  of  a  typical  power  house  in 
which  impulse  wheels  are  installed.  Speed  regulation  of 
the  prime  movers  is  accomplished  by  deflecting  the  nozzles 
past  the  buckets  and  allowing  part  of  the  water  to  impinge 
upon  heavy  metal  deflector  plates. 

Frequently  hydraulic  developments  have  auxiliary  steam 
or  gas  engine  plants  to  supplement  the  water  power  during 
the  dry  seasons  or  during  periods  of  peak  loads. 

100.  Cost  of  Development. — The  cost  of  a  proposed 
hydraulic  development  depends  largely  upon  the  extent  to 
which  the  stream  flow  is  to  be  developed,  upon  the  nature 
and  remoteness  of  the  power  market,  as  well  as  upon 
various  topographical,  geological,  and  meteorological  con- 
ditions of  the  locality.  The  decision  as  to  the  commercial 
feasibility  of  a  proposed  water-power  development  must 
embrace  a  careful  study  of  all  such  factors  which  influence 
water  supply,  of  the  available  head  and  its  variations,  of 
the  power  available  with  and  without  pondage,  of  the 


294 


TRACTION   AND   TRANSMISSION. 


HYDRAULIC   STATIONS. 


295 


location  and  extent  of  the  hydraulic  construction  and 
power  house,  of  the  probable  market  for  the  power  gener- 
ated and  its  load  factor,  and  the  desirability  of  auxiliary 
power. 

Rough  estimates  in  terms  of  generator  capacity  of  the 
cost  of  turbine  equipments  may  be  derived  from  Figs.  125 
and  126,  which  embody  data  from  existing  installations. 


40 


60  80 

HEAD  IN  FEET- 

Pig.  125. 


100 


120 


The  figures  refer  to  reaction  turbines  and  impulse  wheels 
respectively,  and  include  extra  movers  for  exciter  units, 
governors,  and  cost  of  erection. 

The  following  table,  given  by  O.  S.  Lyford,  gives  the  item- 
ized cost  (estimated  or  actual)  per  kilowatt  of  generator 
capacity  of  seven  separate  water-power  developments  in 
the  same  general  district  in  our  southeastern  states,  these 
powers  being  developed  with  heads  varying  from  30  to  120 
feet,  and  with  generator  capacity  varying  from  10,000  to 


296 


TRACTION  AND   TRANSMISSION, 
•a 

v  a 

111 


w         10 

O  ^"  X>-   M     M     IOO     Tf    ^*    CO 


co  O    O  OO  00 


*>•  VO  r^-OO  VO 


M  10    COO     M 


O          O          OOO-NOOO 
M         O         OO<Nr^Ocoo 


M  CO  M     (N     M  M 


3 

<u     ..^ 


o 

'   O 


'C^tSS  B-g  W-Sjl  S 

• 


& 


per 


HYDRAULIC   STATIONS. 


297 


30,000  K.W.  The  appended  column  gives  the  average  of 
the  proportional  costs  of  the  general  groups  for  the  seven 
plants. 


16 
12 
8 

( 

\ 

\ 

k 

\ 

\ 

\ 

\ 

-s'0n 

"- 

\ 

X/O 

^ 

V, 

*Sj 

——  ^^^ 

*-~ 

-—  ^ 

•  —  •  —  . 

•  

)               400            800            1200           1600 
HEAD  IN  FEET. 

Fig.  ia6. 

101.  Depreciation  and  Obsolescence.  —  It  is  difficult  to 
predetermine  with  accuracy  the  cost  of  repairs  essential  to 
maintain  the  various  parts  of  an  installation  in  operating 
condition,  the  time  that  these  parts  will  endure  before  it 
becomes  unwise  to  repair  them,  and  the  time  which  will 
elapse  before  it  will  prove  more  economical  to  substitute 
for  them  more  efficient  parts.  It  is  necessary,  however,  to 
attempt  to  make  such  predeterminations  in  order  to  carry 
out  an  economic  design.  The  following  values  in  reference 
to  hydraulic  plants  are  those  given  by  Dr.  Gary  T.  Hutch- 
inson.  He  also  states  that  the  general  consensus  of  opinion 
as  to  the  depreciation  of  steam  generating  plants  is  that  it 
amounts  to  from  5  per  cent  to  7.5  per  cent,  with  an  addi- 
tional like  value  for  obsolescence.  The  basis  of  the  follow- 


298 


TRACTION  AND   TRANSMISSION. 


ing  table  is  the  assumed  life  and  annual  charges  compounded 
at  the  rate  of  4.5  per  cent.  The  depreciation  in  terms  of 
the  total  cost  assumes  that  the  cost  of  the  power  house, 
the  transmission  line,  and  the  substation  amounts  to  but 
57  per  cent  of  the  total  cost. 


DEPRECIATION   RATES. 


Item. 

Propor- 
tional cost. 

Life 
years. 

Annual  amount 
for  depreciation 
in  per  cent  of 
total  cost. 

POWER  HOUSE: 
i.   Stop  logs,  gates,  and  other  wood 
exposed  to  air  and  water  
2.    Flooring,  roofing  and  hardware, 
and  miscellaneous  fixtures  .... 
3.   Tile  wainscoting,  sewage,  plumb- 
ing system,  and  metal  window 
frames   etc 

0.80 
9.80 

2   4< 

[IQ] 

5 
15 

ie 

0.146 
0.472 

o  118 

4.    Electric  light  and  telephone  .... 
5.    Switchboard  equipment  

0.80 
4.35 

10 
10 

0.065 
0.355 

6.    Cables  and  heavy  wiring  

3  .90 

IO 

0.318 

7     Cranes 

I    2Z 

1C 

o  060 

8     Water  wheels 

72   vc 

2C, 

o  7^:7 

o     Water-wheel  governors 

2    QO 

IO 

O    231? 

TO.    Generators  and  transformers  

4O.OO 

25 

0.898 

TRANSMISSION  LINE: 
i     Right  of  way 

IOO.OO 

Af  . 

[26] 

3-423 

2.   Towers  

18.4 

15 

0.885 

3.    Special  structures  

5-  x 

IO 

0.415 

4     Insulators 

2  .  I 

IO 

o.  170 

5     Copper 

23  .  7 

2C, 

o.  530 

6     Installation 

c  .  7 

SUBSTATION  : 
i     Land 

IOO.O 

6.0 

[20] 

2.OOO 

2     Buildings 

30. 

2C, 

0.67 

3     Transformers 

40 

2O 

1.28 

4     Switches,  etc. 

16. 

IO 

I  .  2O 

5     Installation 

8 

TOO. 

3-24 

HYDRAULIC   STATIONS. 


299 


102.  Relative  Operating  Expenses.  —  The  following 
table,  due  to  H.  G.  Stott,  is  applicable  to  plants  having  a 
maximum  load  of  over  30,000  K.W.,  and  gives  operating 
expenses  and  probable  fixed  charges  based  upon  5  per  cent 
interest,  i  per  cent  for  taxes  and  general  administrative 
expenses,  and  5  per  cent  amortization  or  obsolescence  in 
the  steam  and  hydraulic  plants. 

RELATIVE  COSTS  PER  KILOWATT-HOUR. 


i 

2 

3 

4 

5 

6 

M 

t3 

a 

a  ^  s 

l| 

I 

Items. 

Is 

•g 

'iis  §  "« 

I 

SI 

0 

|| 

B 

^•ii 

•Q 

G 

6 

11 

1 

£§ 

i 

w'Sbp. 

8 

%V 

*>. 

K 

Cfl 

tf 

O 

O 

w 

MAINTENANCE 

i.    Engine  room,  mechanical.  ...... 

2-59 

0-51 

1-55 

5.18 

2.84 

0-51 

2.    Boiler  or  producer  room  

4  ^5 

4   33 

3  55 

i  16 

I    07 

3.   Coal-and  ash-handling  apparatus 

0.58 

0-54 

0.44 

o.  29 

o.  29 

4.    Electrical  apparatus  

i   13 

i   13 

I    13 

1.13 

I    13 

1  .  13 

OPERATION 

5.    Coal  

61  .  70 

--   -. 

C2    AA 

26.52 

25  .97 

6     Water 

7  20 

o  65 

o  61 

3    60 

2    l6 

7.    Engine-room  labor  

6.75 

1.36 

4.06 

6.76 

4.06 

1.36 

8.    Boiler-  or  producer-room  labor. 

7.20 

6.74 

5.50 

1.81 

3  -O1? 

9.    Coal-  and  ash-handling  labor  .  . 

2.28 

2.13 

i-75 

1.14 

1.14 



10.    Ash  removal  

I     O7 

O   QS 

o  81 

o  54 

o  54 

ii.    Electrical  labor  •  

2-54 

2.54 

2-54 

2-54 

2-54 

2-54 

12.    Engine-room  lubrication  

1.78 

o-35 

i  .02 

i.  80 

1.07 

O.2O 

13     Engine-room  waste,  etc 

o  30 

o  30 

o  30 

o  30 

O    3O 

O    2O 

14.    Boiler-room  lubrication,  etc  — 

0.17 

0.17 

0.17 

0.17 

0.17 

Relative  operating  cost,  per  cent.  .  . 

IOO.OO 

77-23 

75-87 

52-94 

47.23 

5-94 

Relative  investment,  per  cent  

100.00 

75.00 

80.00 

IIO.OO 

96.  2O 

IOO.OO 

Probable  average  cost,  per  K.W.($) 
Probable  fixed  charges  

125.00 

11% 

93-75 

IOO.OO 

11% 

137.50 

12% 

I  2O.OO 

n-5% 

125.00 

11% 

103.   Costs  per   Kilowatt-hour.  —  The   average  annual 
cost  per  kilowatt-hour  of  output  depends  upon  the  annual 


3oo 


TRACTION  AND   TRANSMISSION. 


load  factor  and  upon  the  type  of  an  installation.  The  an- 
nual load  factor  is  the  ratio  of  the  annual  output  in  kilo- 
watt-hours to  8760  times  the  rated  capacity  of  the  installed 
apparatus  in  kilowatts.  Since  the  fixed  charges  are  de- 
pendent upon  the  rated  capacity  but  independent  of  the 

60 


0.2 


O.4  0.6 

LOAD  FACTOR. 

Fig.  127. 


O.8 


output,  whereas  the  operating  expenses  are  dependent  upon 
the  latter  and  independent  of  the  former,  the  cost  per  kilo- 
watt-hour of  output  will  be  a  minimum  for  a  load  factor  of 
unity.  Furthermore,  for  a  typical  railway  load  of  a  given 
maximum  demand  the  rating  of  the  power-station  equip- 
ment necessarily  installed  to  meet  this  demand  differs  with 
the  type  of  the  installation.  This  is  due  to  differences  in 


HYDRAULIC   STATIONS.  301 

overload  capacity.  The  necessary  capacity  progressively 
increases  as  the  type  changes  from  steam  to  gas  and  steam 
again  to  hydraulic  or  to  gas  alone. 

For  a  complete  discussion  of  this  subject  the  reader  is 
referred  to  Mr.  Stott's  paper  (Trans.  A.  I.  E.  E.,  xxviii, 
p.  1479),  from  which  Fig.  127  is  taken.  This  figure  shows 
the  dependence  of  the  total  annual  cost  per  installed 
kilowatt  upon  the  load  factor  and  the  type  of  plant.  The 
titles  associated  with  the  various  lines  refer  to  the  col- 
umns in  the  table  of  the  preceding  article,  each  of  which 
represents  a  definite  type  of  installation.  A  low  grade  of 
coal,  costing  #1.50  per  ton  and  giving  11,000  B.t.u.  per 
pound,  has  been  assumed.  The  average  cost  per  kilowatt- 
hour  may  be  determined  by  dividing  the  value  of  any 
ordinate  by  8760  times  the  corresponding  load-factor. 

PROBLEMS. 

48.  Determine  the  proper  size  and  number  of  steam  turbo-generator  units 
for  a  power  station  having  a  load  curve  of  the  form  indicated  in  Fig.  107 
but  with  ordinates  of  half  the  value.    What  would  be  the  probable  number 
of  daily  hours  of  operation  of  each  unit  ? 

49.  If  the  turbines  of  problem  48  consume  17  pounds  of  dry  saturated 
steam  at  175  pounds  gauge  pressure  per  kilowatt-hour  and  if  the  auxiliaries 
use  10  per  cent  of  the  total  steam  generated,  how  many  boilers  should  be 
installed  per  unit  and  what  should  be  the  horsepower  of  each  ?     Assume 
the  temperature  of  feed  water  to  be  80°  F. 

50.  Determine  the  diameter  of  the  runners  for  a  twin  reaction  turbine  to 
operate  on  a  loo-foot  head  for  a  sooo-kilowatt,  25-cycle,  three-phase  alter- 
nator, whose  efficiency  is  96  per  cent.     The  constants  of  the  turbine  are 

K  =  3.0 

T    =    0.74 
€    =    0.8S 


INDEX. 


(The  figures  refer  to  page  numbers.) 


Acceleration,  21. 

automatic,  108. 

curve,  53,  57.      . 

rates,  changes  in,  126. 
Adequacy  of  copper  distribution,  150. 
Adhesion,  coefficient  of,  50. 
Adjustment  of  speed  curves,  66. 
Alternating-current  control,  89. 
distribution,  164. 
motors,  27. 
substations,  166. 
Annual  car-miles  operated,  5. 
Apparatus,  arrangement  of  station, 

189,  275. 

Arc  suppressor,  256. 
Arresters,  lightning,  209,  255. 
Atmospheric  heaters,  272. 

potential  differences,  252. 
Attenuation  constant,  238. 
Automatic  acceleration,  108. 
Auxiliary  feeders,  151. 

storage  batteries,  188. 
Average  current  per  car,  112. 

Batteries,  storage,  188. 
Bearing  friction,  15. 
Boilers,  270. 
Bonds,  track,  156. 
Boosters,  152. 
Braking,  22. 

curve,  52,  58. 

energy  lost  in,  126. 
Branches  in  roadway,  139. 

Cables,  resistance  of,  221. 
Capacity  of  lines,  230. 

of  motors,  51. 
Car-body,  types  of,  9. 
-mile,  earnings  per,  6. 


Car-miles,  annual,  5. 
Car  cross  sections,  17. 

equipments,  weights  of,  55. 

number  of,  for  urban  road,  4. 

propulsion,  tractive  effort  for, 

15- 

size  of,  8. 

Cascade  control,  99. 
Center  feeding  of  sections,  138. 

of  distribution,  199. 
Charging  current  of  line,  247. 
Chimneys,  272. 
Choke  coils,  209,  255. 
Classification  of  conductors,  133. 
Closed  cars,  9. 
Coasting  curve,  52,  58. 

effect  of  changes  in,  129. 
Coefficient  of  adhesion,  23,  50. 
Collecting  devices,  140. 
Compensated  series  motors,  35. 
Compensators,  91. 

multiple-switch,  93. 
Compounded  converters,  172. 
Condensers,  267. 
Conductive  compensation,  36. 
Conductor  separation,  213. 
Conductors,  resistance  of,  220. 

weights  of,  202,  220. 
Connecting-rod  drive,  40. 
Contact  conductors,  134. 
Continuous  capacity  of  motors,  119. 
Control,  alternating-current,  89. 

apparatus,  weights  of,  55. 

cascade,  99. 

compensator,  91. 

direct-current,  74. 

hand,  102. 

induction  motor,  95. 
regulator,  89. 


303 


3°4 


INDEX. 


Control,  methods  of,  74. 

multiple-unit,  104. 

rheostatic,  74. 

series-parallel,  75. 
Controllers,  102. 
Converter,  characteristics  of,  171. 

substations,  169. 

-transformer  deficiencies,  183. 
Convertible  cars,  9. 
Cooling  towers,  269. 
Copper  loss  of  motor,  118. 
Corona,  214. 

loss,  247. 

Corrosion,  electrolytic,  157. 
Cost  constants,  185. 

of  electrical  energy,  299. 

of  hydraulic  development,  293. 
movers,  295. 

of  steam  stations,  279. 

of  substation  units,  174. 

of  transformers,  208. 
Crest  factor,  definition  of,  218. 
Critical  line  voltage,  213. 
Cross  section  of  contact  conductor, 

J35- 

of  feeder,  151. 
of  line  conductor,  206. 
of    supplementary    conductor, 

143- 
Current,  average,  per  car,  112. 

curves,  in. 

density,  economic,  152. 

distribution  on  lines,  240. 

effective,  motor,  113. 

-limit  relay,  109. 
Curves  in  roadway,  19. 

Daily  load  diagrams,  180. 

Dams,  288. 

Data  for  plotting  speed  curves,  53. 

Deficiency  constants,  184. 

Degree  of  track  curvature,  20. 

Depreciation  of   generating  plants, 

297. 

Design  of  controller  units,  79. 
Developments,  hydraulic,  288. 

cost  of,  293. 
Direct-current  control,  74. 

motors,  26. 

transmission,  166. 
Distance  curves,  66. 


Distributing  system,  133. 
Distribution  of  current  on  lines,  240. 
Diversity  factor,  210,  260. 
Double-decked  cars,  9. 

stations,  275. 
Drive,  methods  of,  40. 
Duration  of  stops,  56. 

Earnings  per  car-mile,  5. 
Economic  current  density,  152. 

section  of  contact  conductor,  135, 
177. 

spacing  of  substations,  176. 

transmission  voltage,  205. 
Economizers,  272. 
Effective  motor  current,  113. 

per  trip,  116. 
Effect   of   operating   conditions   on 

energy  consumption,  124. 
Efficiency  of  hydraulic  movers,  285. 

of  substation  apparatus,  170. 

of  transformers,  168,  203. 

of  transmission,  246. 
Electrical  energy,  cost  of,  299. 
Electric    field    intensity    near    con- 
ductors, 214. 
Electrolytic  corrosion,  157. 

surveys,  161. 
E.M.F.    equation    of    single-phase 

motors,  32,  37. 
Elevation  of  outer  rail,  20. 
End  feeding  of  sections,  137. 
Energy  consumption,  in. 

effect  of  operation  on,  124. 

for  car  propulsion,  120. 
Engineer's  problem,  i. 
Engines,  steam,  265. 
Equations    of    wave    propagation, 

235- 
Equivalent  hours  of  operation,  182 

line  length,  211. 
Expenses  per  car-mile,  6. 
Extension  factor,  218. 

Feeders,  151. 

negative,  157. 
Feed- water  heaters,  272. 
Fixed  charges  of  power  station,  264. 
Floor  space  in  power  stations,  274. 

in  substations,  170. 
Forced  compensation,  36. 


INDEX. 


305 


Frequency,  203. 

resonant,  of  line,  204. 
Friction,  coefficient  of,  23. 

Gas  engines,  264. 
Gates  for  turbines,  282. 
Gear  drive,  40. 

ratio,  choice  of,  56. 

effect  on  acceleration  rate,  131. 
Generators  for  power  station,  261. 
Governors  for  hydraulic  movers,  284. 
Grades,  19. 

Graphic  time-tables,  147. 
Grid  resistances,  80. 
Ground  wires,  257. 

Hand  control,  102. 
Heating  of  motors,  51,  118. 
Heights  of  chimneys,  273. 
Horsepower  rating  of  motors,  119. 
Hydraulic  construction,  288. 

power  stations,  281. 
Hyperbolic  functions,  224. 

Impedance  of  rails,  164. 
Impulse  wheels,  281. 
Income  of  electric  railways,  5. 
Inductance  of  lines,  222. 
Induction  motor,  39. 
control  of,  95. 

regulators,  89. 

Inductive  compensation,  36. 
Ingredients  of  third  rails,  136. 
Installations,  substation,  cost  of,  175. 
Insulators,  207. 

Internal  combustion  engines,  264. 
Interurban  road,  cars  for,  13. 
lonization  of  air,  215. 
Iron  loss  of  motor,  118. 

pipes,  resistance  of,  163. 

Jet  condensers,  268. 

Leakage  current,  157. 

Leakance,  line,  237. 

Length  of  average  passenger  ride,  8. 

of  track  for  urban  road,  2. 
Lightning,  252. 

arresters,  209,  255. 

protection,  254. 
Limitations  of  motors,  50. 


Line  capacity,  230. 

inductance,  222. 

leakance,  237. 

resistance,  220. 
Load  curves,  180,  259. 
Location  of  substations,  175. 

of  transmission  line,  199. 
Locomotives,  electric,  39. 
Losses  in  motors,  118. 

in  substations,  184. 

Master  controllers,  105. 
Mechanical  draft  apparatus,  273. 
Methods  of  drive,  40. 
Mixed-flow  turbine,  281. 
Motor  capacity,  51. 

characteristic  curves,  43. 

control,  74. 

effective  current,  113. 

-generator  substations,  170. 

heating,  51,  118. 

limitations,  50. 

output,  48. 

saturation  curve,  79,  87. 
Motors,  alternating-current,  27 

compensated  series,  35. 

direct-current,  26. 

induction,  39. 

railway,  25. 

repulsion,  38. 

series,  26,  29. 

weights  of,  55. 

Moutiers-Lyons  transmission,  166. 
Multiple-switch  compensator,  93. 

-unit  control,  13. 

Narragansett  type  of  car,  10. 
Negative  conductors,  133. 

track  feeders,  157. 
Nominal  rating  of  motors,  119. 
Number  of  cars  for  urban  road,  4. 

of  units  in  substations,  180. 
Numerical  examples,  12,  18,  59,  67, 
87,  113,  127,  186,  205,  211, 
219,  244,  250,  287. 

Obsolescence  of  generating  plants, 

297. 

Oil  switches,  cost  of,  209. 
Open  cars,  9. 


306 


INDEX. 


Operating    characteristics    of    con- 
verters, 171. 

of  motor-generators,  172. 
conditions,  changes  in,  124. 
expenses  of  power  stations,  264, 

280,  299. 
of  railways,  6. 

Output  of  power  stations,  261. 
Overload  capacity  of  generators,  182, 

263.    ' 

coefficient,  180. 
Overrunning  third  rail,  141. 

Pantograph  frames,  141. 
Passenger  factor,  3. 
Passengers  per  trip,  8. 
Pay-as-you-enter  cars,  10. 
Performance  curves  of  motors,  43. 
Phases,  number  of,  201. 
Pipes,  resistances  of,  163. 
Plotting  speed  curves,  56. 

with  grades  and  curves,  67. 
Poles,  transmission,  207. 

trolley,  140. 

Population  served  by  railway,  4. 
Portable  substations,  194. 
Positive  conductors,  133. 
Power  factor  curves,  122. 

of    series    single-phase    motors, 

33,  37- 

lost  in  conductors,  138. 
-station  buildings,  274. 
costs,  264,  279. 
location  of,  200. 
output,  261. 
Preventive  coils,  92. 
Prime  movers,  types  of,  263. 
Problems,  14,  24,  49,  72,  109,  132, 

164,  197,  257,  301. 
Propagation  of  electric  waves,  235. 
Protection  from  lightning,  254. 
Pumps  for  steam  stations,  268. 

Quill  drive,  43. 

Rails,  155. 

impedance  of,  164. 
Rates  of  acceleration,  22. 

of  braking,  53. 
Reactance  set,  172. 
Receipts  of  electric  railway,  4. 


Regeneration  of  energy  with  induc- 
tion motors,  39. 
Regulation  of  converters,  171. 

of  transmission  line,  243. 
Regulators,  induction,  89. 
Relative  operating  expenses  of  gen- 
erating plants,  299. 

weights  of  conductors,  202. 
Relay,  current-limit,  109. 
Repulsion  motors,  38. 
Resistance  of  conductors,  220. 

offered  to  car  movement,  15. 

of  iron  pipes,  163. 

of  third  rails,  136. 

of  track  rails,  156. 

to  alternating  currents,  221. 
Resistances,  motor  starting,  78. 
Resonant  currents,  254. 

frequency  of  line,  204. 
Retardation,  23. 
Rheostatic  control,  74. 
Ride,  average  passenger,  8. 
Rights  of  way,  200. 
Roadway,  characteristics  of,  56. 
Rolling  friction,  15. 

Saturation  curve  of  motors,  79,  87. 
Schedule  speeds,  13,  56. 
Scott  transformer  connection,  28, 169. 
Seating  capacity  of  cars,  9. 
Seats,  arrangement  of,  10. 
Sectional  contact  conductors,  138. 
Selection  of  gear  ratio,  56. 

of  generator  units,  261. 
Semiconvertible  cars,  9. 
Separation  of  line  conductors,  213. 
Series-parallel  control,  75. 

-wound  motors,  26,  29. 
Service,  railway,  types  of,  i. 
Single-phase  railway  motors,  29. 
Size  of  cars  for  urban  road,  8. 
Skin  effect,  221. 

resistance  of  rails,  164. 
Speed  curves,  50. 

of  car,  51. 

of  hydraulic  movers,  287. 

of  motor,  25,  48. 
Stacks,  272. 

Standard  transmission  voltages,  212. 
Starting  resistances,  78. 
energy  lost  in,  125. 


INDEX. 


307 


Station  load  curves,  259. 
Steam,  265. 

power  stations,  265. 
Stops,  duration  of,  56. 
Storage  batteries,  188. 
Striking  distance,  216. 
Substations,  166. 

arrangement  of  apparatus  in,  189. 

cost  of,  175. 

efficiency  of  apparatus  in,  170. 

floor  space  in,  170. 

location  of,  175. 

number  of  units  in,  180. 

portable,  194. 

connections  of,  197. 
Superheaters,  266. 
Supplementary  conductors,  142. 
Surface  condensers,  268. 
Surges  from  lightning,  253. 
Surveys,  electrolytic,  161. 
Synchronous    speed    of    induction 
motors,  96. 

Table  of  hyperbolic  functions,  228. 
Temperature   elevation   of   motors, 

119. 
Third  rails,  composition  of,  136. 

resistance  of,  136. 
Three-phase  railway  motors,  39. 

-point  grid  resistance,  80. 
Thury  transmission  system,  166. 
Time-tables,  graphic,  148. 
Total  drop  in  conductor,  135. 
Towers,  transmission,  207. 
Track  factor,  3. 

feeders,  157. 

length  of,  for  urban  road,  2. 

rails,  155. 

Traction  motors,  25. 
Tractive  effort,  15,  48. 

-speed  curve,  60. 
Train  resistance,  15. 

-sheets,  148. 

Trains  for  interurban  service,  13. 
Transformer  efficiencies,  168,  203. 


Transformers,  costs  of,  208. 

weights  of,  203. 
Transmission  lines,  199. 
Trip,  motor  current  per,  116. 
Trolley  wheels,  140. 

wires,  135. 
Turbines,  hydraulic,  281. 

steam,  265. 

Types  of  prime  movers,  263. 
Typical  speed  curves,  52. 

Underrunning  third  rail,  142. 
Units,  controller  resistance,  79. 

generator,  262. 
Urban  road,  cars  for,  i. 

Vacuum  heaters,  272. 

pumps,  268. 

Variable  polarity  induction  motor 
control,  96. 

resistance   induction   motor   con- 

_  trol,  95. 
Velocity  of  car,  51. 

of  wave  propagation,  243. 
Voltage  along  roadway,  129. 

critical,  213. 

curves,  118. 

distribution  on  lines,  240. 

of  boosters,  154. 

regulation,  243. 

transmission,  economic,  205. 

Wages  of  substation  attendants,  178. 
Water-power  development,  288. 

wheels,  284. 

Watts  lost  in  conductor,  138. 
Wave-length  coefficient,  238. 

propagation  along  wires,  235. 
Weights  of  car  equipments,  54. 

of  cars,  ii. 

of  conductors,  relative,  202. 

of  iron  pipe,  163. 

of  transformers,  203. 
Wheels,  trolley,  140. 
Wind  resistance,  16. 


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LORING,  A.  E.  A  Handbook  of  the  Electro-Magnetic  Telegraph. 
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MAILLOUX,  C.  0.  Electric  Traction  Machinery.  Illustrated.  8vo., 
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'MUNRO,  J.,  and  JAMIESON,  A.  A  Pocket-Book  of  Electrical  Rules  and 
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OHM,  G.  S.  The  Galvanic  Circuit  Investigated  Mathematically.  Berlin, 
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SCHELLEN,  H.  Magneto-Electric  and  Dynamo-Electric  Machines.  Their 
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WALLING,  B.  T.,  and  MARTIN,  JULIUS.  Electrical  Installations  of  the 
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WALMSLEY,  R.  M.  Electricity  in  the  Service  of  Man.  A  Popular  and 
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WEEKS,  R.  W.      The  Design  of  Alternate-Current  Transformer. 

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WEYMOUTH,  F.  MARTEN.  Drum  Armatures  and  Commutators. 
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WILKINSON,  H.  D.  Submarine  Cable  Laying,  Repairing  and  Testing. 
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YOUNG,  J.  ELTON.  Electrical  Testing  for  Telegraph  Engineers.  Illus- 
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